About the lattice of pretopologies on an set X
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Universidad Industrial de Santander
Abstract
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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.
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.
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, ultratopolo-gies, retículo, pretopologías, esqueletos de retículos completos, ultratopologías