<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2022000200159</article-id>
<article-id pub-id-type="doi">10.18273/revint.v40n2-2022002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Properties of the (n, m)&#8722;fold hyperspace suspension of continua]]></article-title>
<article-title xml:lang="es"><![CDATA[Propiedades del (n, m)&#8722;ésimo hiperespacio suspensión de continuos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HERNÁNDEZ-VALDEZ]]></surname>
<given-names><![CDATA[GERARDO]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HERRERA-CARRASCO]]></surname>
<given-names><![CDATA[DAVID]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[LÓPEZ]]></surname>
<given-names><![CDATA[MARÍA DE J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MACÍAS-ROMERO]]></surname>
<given-names><![CDATA[FERNANDO]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>40</volume>
<numero>2</numero>
<fpage>159</fpage>
<lpage>168</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2022000200159&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2022000200159&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2022000200159&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. Let n, m &#8712; N with m &#8804; n and X be a metric continuum. We con-sider the hyperspaces C  n (X) (respectively, F  n (X)) of all nonempty closed subsets of X with at most n components (respectively, n points). The (n, m)&#8722;fold hyperspace suspension on X was introduced in 2018 by Anaya, Maya, and Vázquez-Juárez, to be the quotient space C  n (X)/F  m (X) which is obtained from C  n (X) by identifying F  m (X) into a one-point set. In this paper we prove that C  n (X)/F  m (X) contains an n&#8722;cell; C  n (X)/F  m (X) has prop-erty (b); C  n (X)/F  m (X) is unicoherent; C  n (X)/F  m (X) is colocally connected; C  n (X)/F  m (X) is aposyndetic; and C  n (X)/F  m (X) is finitely aposyndetic.  MSC2010:  54B20, 54F15.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. Sean n, m &#8712; N con m &#8804; n y X un continuo métrico. Conside-ramos el hiperespacio de todos los subconjuntos cerrados, no vacíos de X con a lo más n componentes (respectivamente, n puntos) C  n (X) (respecti-vamente, F  n (X)). El (n, m)&#8722;ésimo hiperespacio suspensión de X lo intro-dujeron, en 2018, Anaya, Maya y Vázquez-Juárez, como el espacio cociente C  n (X)/F  m (X) que se obtiene de C  n (X) al identificar F  m (X) a un conjunto de un punto. En este artículo demostramos que C  n (X)/F  m (X) contiene una n&#8722;celda; C  n (X)/F  m (X) tiene la propiedad (b); C  n (X)/F  m (X) es unicohe-rente; C  n (X)/F  m (X) es colocalmente conexo; C  n (X)/F  m (X) es aposindético y C  n (X)/F  m (X) es finitamente aposindético.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Aposyndesis]]></kwd>
<kwd lng="en"><![CDATA[Cantor manifold]]></kwd>
<kwd lng="en"><![CDATA[Continuum]]></kwd>
<kwd lng="en"><![CDATA[Colocal connected-ness]]></kwd>
<kwd lng="en"><![CDATA[(n]]></kwd>
<kwd lng="en"><![CDATA[m)&#8722;fold hyperspace suspension]]></kwd>
<kwd lng="en"><![CDATA[Property (b)]]></kwd>
<kwd lng="en"><![CDATA[Unicoherent]]></kwd>
<kwd lng="es"><![CDATA[Aposindesis]]></kwd>
<kwd lng="es"><![CDATA[Continuo]]></kwd>
<kwd lng="es"><![CDATA[Colocalmente conexo]]></kwd>
<kwd lng="es"><![CDATA[(n]]></kwd>
<kwd lng="es"><![CDATA[m)&#8722;ésimo hiperespacio suspensión]]></kwd>
<kwd lng="es"><![CDATA[Propiedad (b)]]></kwd>
<kwd lng="es"><![CDATA[Variedad de Cantor]]></kwd>
<kwd lng="es"><![CDATA[Unicoherente]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Anaya]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Maya]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Vázquez-Juárez]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The hyperspace HSmn(X) for a finite graph X is unique]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2018</year>
<volume>234</volume>
<page-range>428-39</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bennett]]></surname>
<given-names><![CDATA[D.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Aposyndetic properties of unicoherent continua]]></article-title>
<source><![CDATA[Pacific J. Math]]></source>
<year>1971</year>
<volume>37</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>585-9</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Curtis]]></surname>
<given-names><![CDATA[D.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Nhu]]></surname>
<given-names><![CDATA[N.T]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hyperspaces of finite subsets which are homeomorphic to &#8501;0&#8722;dimensional linear metric spaces]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>1985</year>
<volume>19</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>251-60</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dugundji]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Topology]]></source>
<year>1978</year>
<edition>2</edition>
<publisher-loc><![CDATA[Moscow, Idaho, USA ]]></publisher-loc>
<publisher-name><![CDATA[BCS Associates]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Escobedo]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the hyperspace suspension of a continuum]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[López M. de]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<source><![CDATA[Topology Appl]]></source>
<year>2004</year>
<volume>138</volume>
<numero>1-3</numero>
<issue>1-3</issue>
<page-range>109-24</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Uniqueness of the (n, m)&#8722;fold hyperspace suspension for continua]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[López M]]></surname>
<given-names><![CDATA[de J]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R]]></given-names>
</name>
</person-group>
<source><![CDATA[Topol. Appl]]></source>
<year>2015</year>
<volume>196</volume>
<page-range>652-67</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dendrites with unique hyperspace]]></article-title>
<source><![CDATA[Houston J. Math]]></source>
<year>2007</year>
<volume>33</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>795-805</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Illanes]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Finite graphs have unique hy-perspace HSn(X)]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Vázquez]]></surname>
<given-names><![CDATA[F.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Top. Proc]]></source>
<year>2014</year>
<volume>44</volume>
<page-range>75-95</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
<name>
<surname><![CDATA[López M]]></surname>
<given-names><![CDATA[de J]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Framed continua have unique n&#8722;fold hyperspace suspension]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2015</year>
<volume>196</volume>
<page-range>652-67</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
<name>
<surname><![CDATA[López M]]></surname>
<given-names><![CDATA[de J]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Almost meshed locally connected continua without unique n&#8722;fold hyperspace suspension]]></article-title>
<source><![CDATA[Houston J. Math]]></source>
<year></year>
<volume>44</volume>
<numero>2018</numero>
<issue>2018</issue>
<page-range>1335-65</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Illanes]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nadler]]></surname>
<given-names><![CDATA[S.B]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hyperspaces Fundamentals and Recent Advances]]></article-title>
<source><![CDATA[Taylor &amp; Francis]]></source>
<year>1999</year>
<volume>216</volume>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kuratowski]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<source><![CDATA[Topology]]></source>
<year>1968</year>
<volume>2</volume>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sternfeld]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The space of subcontinua of a 2-dimensional continuum is infinitely dimensional]]></article-title>
<source><![CDATA[Proc. Amer. Math. Soc]]></source>
<year>1997</year>
<volume>125</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>2771-5</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Libreros-López]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the uniqueness of n&#8722;fold pseudo-hyperspace suspension for locally connected continua]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year></year>
<volume>312</volume>
<numero>2022</numero>
<issue>2022</issue>
<page-range>1-22</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[J.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the n&#8722;fold pseudo-hyperspace suspensions of continua]]></article-title>
<source><![CDATA[Glas. Mat. Ser. III]]></source>
<year>2008</year>
<volume>43</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>439-49</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the hyperspaces Cn(X) of a continuum X]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2001</year>
<volume>109</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>237-56</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the n&#8722;fold hyperspace suspension of continua]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2004</year>
<volume>138</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>125-38</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the n&#8722;fold hyperspace suspension of continua, II&#8221;]]></article-title>
<source><![CDATA[Glas. Mat. Ser. III]]></source>
<year>2006</year>
<volume>41</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>335-43</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<source><![CDATA[Topics on continua, Springer Cham]]></source>
<year>2018</year>
<edition>2</edition>
</nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Jr. S.B]]></surname>
<given-names><![CDATA[Nadler]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[n&#8722;fold hyperspace, cones, and products]]></article-title>
<source><![CDATA[Topology Proc]]></source>
<year>2001</year>
<volume>26</volume>
<page-range>255-70</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montero]]></surname>
<given-names><![CDATA[G.R.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
<name>
<surname><![CDATA[López M]]></surname>
<given-names><![CDATA[de J]]></given-names>
</name>
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[F.R]]></given-names>
</name>
</person-group>
<source><![CDATA[Finite graphs have unique n&#8722;fold symmetric product suspension]]></source>
<year>2019</year>
<numero>47</numero>
<conf-name><![CDATA[ 34Summer Conference on Topology and its Applications]]></conf-name>
<conf-loc>Johannesburg, South Africa </conf-loc>
<issue>47</issue>
</nlm-citation>
</ref>
<ref id="B22">
<label>[22]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Morales]]></surname>
<given-names><![CDATA[U.F]]></given-names>
</name>
</person-group>
<source><![CDATA[Finite graphs have unique n&#8722;fold pseudo-hyperspace suspension]]></source>
<year>2015</year>
<numero>52</numero>
<conf-name><![CDATA[ 30Summer Topology Conference]]></conf-name>
<conf-loc>Galway, Ireland </conf-loc>
<issue>52</issue>
<page-range>219-33</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>[23]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jr. S.B]]></surname>
<given-names><![CDATA[Nadler]]></given-names>
</name>
</person-group>
<source><![CDATA[Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Mathematics]]></source>
<year>1978</year>
<volume>49</volume>
<publisher-loc><![CDATA[New York, Basel ]]></publisher-loc>
<publisher-name><![CDATA[Marcel Dekker]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<label>[24]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jr. S.B]]></surname>
<given-names><![CDATA[Nadler]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A fixed point theorem for hyperspace suspensions]]></article-title>
<source><![CDATA[Houston J. Math]]></source>
<year>1979</year>
<volume>5</volume>
<page-range>125-32</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>[25]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jr. S.B]]></surname>
<given-names><![CDATA[Nadler]]></given-names>
</name>
</person-group>
<source><![CDATA[Continuum Theory: An Introduction]]></source>
<year>1992</year>
<volume>158</volume>
<edition>1st</edition>
<publisher-name><![CDATA[CRC Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<label>[26]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jr. S.B]]></surname>
<given-names><![CDATA[Nadler]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dimension Theory: An introduction with exercises]]></article-title>
<source><![CDATA[Sociedad Matemática Mexicana]]></source>
<year>2002</year>
<volume>18</volume>
</nlm-citation>
</ref>
<ref id="B27">
<label>[27]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Whyburn]]></surname>
<given-names><![CDATA[G.T]]></given-names>
</name>
</person-group>
<source><![CDATA[Analytic Topology, Amer. Math. Soc. Colloq. Publ]]></source>
<year>1942</year>
<volume>28</volume>
<publisher-name><![CDATA[American Mathematical Society, Providence, RI]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
