<?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>S0120-419X2018000200083</article-id>
<article-id pub-id-type="doi">10.18273/revint.v36n2-2018002</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Sobre el índice de acotamiento de grupos topológicos]]></article-title>
<article-title xml:lang="en"><![CDATA[On the index of boundedness of topological groups]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ramírez-Páramo]]></surname>
<given-names><![CDATA[Alejandro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Tenorio]]></surname>
<given-names><![CDATA[Jesús F.]]></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 de la Electrónica ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Tecnológica de la Mixteca Instituto de Física y Matemáticas ]]></institution>
<addr-line><![CDATA[Oaxaca ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>36</volume>
<numero>2</numero>
<fpage>83</fpage>
<lpage>99</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2018000200083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2018000200083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2018000200083&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. Estas notas proporcionan una breve introducción al índice de acotamiento en grupos topológicos. Damos, de manera casi autosuficiente, las herramientas necesarias de funciones cardinales, así como los hechos básicos de la teoría de grupos topológicos. MSC2010: 54H11, 54A25, 22A05, 54D20.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. These notes provide a brief introduction to the index of boundedness in topological groups. We give, in an almost self-contained way, the necessary tools of cardinal functions, as well as the basic facts of the theory of topological groups.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Función cardinal]]></kwd>
<kwd lng="es"><![CDATA[grupo topológico]]></kwd>
<kwd lng="es"><![CDATA[índice de acotamiento]]></kwd>
<kwd lng="en"><![CDATA[Cardinal function]]></kwd>
<kwd lng="en"><![CDATA[topological group]]></kwd>
<kwd lng="en"><![CDATA[index of boundedness]]></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[Alexandroff]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Urysohn]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mémoire sur les éspaces topologiques compacts]]></article-title>
<source><![CDATA[Ver. Akad. Wetensch]]></source>
<year>1929</year>
<volume>14</volume>
<page-range>1-96</page-range><publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Arhangel'skii]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Topological groups and related structures]]></source>
<year>2008</year>
<publisher-name><![CDATA[Atlantis Studies in Mathematics, Atlantis Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Ginsburg]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Woods]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cardinal inequalities for topological spaces involving the weak Lindelöf number]]></article-title>
<source><![CDATA[Pacific J. Math]]></source>
<year>1978</year>
<volume>79</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>37-45</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Casarrubias-Segura]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramírez-Páramo]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some reflection theorems]]></article-title>
<source><![CDATA[Topology Proc]]></source>
<year>2007</year>
<volume>31</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>51-65</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Charlesworth]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the cardinality of a topological space]]></article-title>
<source><![CDATA[Proc. Amer. Math. Soc]]></source>
<year>1997</year>
<volume>66</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>138-42</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Engelking]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[General topology, Translated from the Polish by the author]]></source>
<year>1989</year>
<edition>2</edition>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Heldermann Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hodel]]></surname>
<given-names><![CDATA[R.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Arhangel'skii's solution to Alexandroff's problem: A survey]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2006</year>
<volume>153</volume>
<numero>13</numero>
<issue>13</issue>
<page-range>2199-217</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hodel]]></surname>
<given-names><![CDATA[R.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cardinal functions I]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Kunen]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Vaughan]]></surname>
<given-names><![CDATA[J. E]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of set-theoretic topology]]></source>
<year>1984</year>
<page-range>1-61</page-range><publisher-loc><![CDATA[North-Holland, Amsterdam ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hodel]]></surname>
<given-names><![CDATA[R.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Vaughan]]></surname>
<given-names><![CDATA[J.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reflection theorems for cardinal functions]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>2000</year>
<volume>100</volume>
<page-range>47-66</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Juhász]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
</person-group>
<source><![CDATA[Cardinal functions in topology-10 years later]]></source>
<year>1980</year>
<publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[Math. Center Tract]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M.G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cellularity and the index of narrowness in topological groups]]></article-title>
<source><![CDATA[Comment. Math. Univ. Carolin]]></source>
<year>2011</year>
<volume>52</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>309-15</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M.G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Introduction to topological groups]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>1998</year>
<volume>86</volume>
<page-range>179-231</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M.G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Paratopological and Semitopological Groups Versus Topological Groups]]></article-title>
<source><![CDATA[Recent Progress in General Topology III]]></source>
<year>2014</year>
<page-range>825-82</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M.G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Topological features of topological groups]]></article-title>
<source><![CDATA[Handbook of the History of General Topology]]></source>
<year>2001</year>
<volume>3</volume>
<page-range>1027-144</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tkachenko]]></surname>
<given-names><![CDATA[M.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Villegas Silva]]></surname>
<given-names><![CDATA[L.M]]></given-names>
</name>
<name>
<surname><![CDATA[Hernández García]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rendón Gómez]]></surname>
<given-names><![CDATA[O.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Grupos topológicos]]></source>
<year>1997</year>
<edition>Primera</edition>
<publisher-name><![CDATA[Autónoma Metropolitana, Unidad Iztapalapa]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Torres Falcón]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Unions of chains of subgroups of a topological group]]></article-title>
<source><![CDATA[Appl. Gen. Topol]]></source>
<year>2001</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>227-35</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
