Acerca del retículo de las pretopologías sobre
un conjunto X

FÉLIX A. PÁEZ DÍAZ^*
Universidad Pontificia Bolivariana, Departamento de Ciencias Básicas, Bucaramanga, Colombia.

Resumen. Mostramos que (Pretop(X),≤), el retículo de las pretopologías sobre un conjunto arbitrario X, siempre tiene un esqueleto, y presentamos una caracterización de los coátomos en Pretop(X) en términos de ultratopologías sobre X.
Palabras claves: retículo, pretopologías, esqueletos de retículos completos, ultratopologías.
MSC2000: 06B30, 54H12, 06F30.

About the lattice of pretopologies on an set X

Abstract. We show that (Pretop(X),≤), the lattice of pretopologies on an arbitrary set X, always has a framework; we present a characterization of the co-atoms in Pretop(X) in terms of ultratopologies on X.
Keywords: lattice, pretopologies, complete lattices frameworks, ultratopologies.

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^*Autor para correspondencia: E-mail : felix.paez@upb.edu.co.
Recibido: 12 de septiembre de 2011, Aceptado: 14 de diciembre de 2011.