Hausdorff closed extensions of pre-uniform spaces

Adalberto García-Máynez

Mexico

Universidad Nacional Autónoma de México

Instituto de Matemáticas

Rubén Mancio-Toledo

Mexico

Instituto Politécnico Nacional

Escuela Superior de Física y Matemáticas

Submitted: 2013-07-29

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Accepted: 2013-07-29

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Published: 2012-04-15

DOI: https://doi.org/10.4995/agt.2012.1635
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Keywords:

Hausdorff closed space, Densely finite-cover, Katetov extension, Round filter

Supporting agencies:

This research was not funded

Abstract:

The family of densely finite open covers of a Hausdorff space X determines a completable pre-uniformity on X and the canonical completion X is Hausdorff closed. We compare X with the Katetov extension kX of X and give sufficient conditions for the non-equivalence of kX and X.
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References:

R. Engelking, General Topology, Polish Scientific Publishers (Warszawa, 1975).

A. García-Máynez and Rubén S. Mancio, Completions of pre-uniform spaces, Appl. Gen. Topol. 8, no. 2 (2007), 213–221.

A. García-Máynez and Rubén S. Mancio, Extending maps between pre-uniform spaces, Appl. Gen. Topol. 13, no. 1 (2012), 21–25.

A. García-Máynez and A. Tamariz, Topología General, Porrúa (México, 1988).

Rubén S. Mancio, Los espacios pre-uniformes y sus completaciones, Ph. D. Thesis, Universidad Nacional Autónoma de México, 2007.

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