Completions 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: 2013-11-15

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Accepted: 2013-11-15

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DOI: https://doi.org/10.4995/agt.2007.1882
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Keywords:

Pre–uniform space, Complete pre–uniform space, Uniform continuity, Pre–uniformity basis, Semi–uniformity basis, Unimorphism, Unimorphism embedding, Equivalent, Admisible and compatible pre–uniformities, Balanced filter, Cauchy, Minimal Cauchy, Round, Weak

Supporting agencies:

This research was not funded

Abstract:

In this paper we prove the existence of a completion of a T0–pre-uniform space (X,U), with the property that each Cauchy filter in (X,U) contains a weakly round filter.
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References:

A. García-Máynez and A. Támariz Mascarúa , Topología General, México., Porrúa, 1988.

R. Mancio-Toledo, Los espacios pre-uniformes y sus completaciones, Ph. D. Thesis, Universidad Nacional Autónoma de México, 2006.

K. Morita, On the simple extension of a space with respect to a uniformity, I, II, III and IV, Proc. Japan Acad. 27 (1951), 65-72, 130-137, 166-171 and 632-636. 14(1953), 68-69, 571.

K. Morita and J. Nagata, Topics in General Topology, Amsterdam, Elsevier Science Publishers B. V., 1989.

R. J. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, New York., Springer-Verlag New York Inc., 1988. https://doi.org/10.1007/978-1-4612-3712-9

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