Completions of pre–uniform spaces

Adalberto García-Máynez, Rubén Mancio-Toledo

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.

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

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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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1. Extending maps between pre-uniform spaces
Adalberto García-Máynez, Rubén Mancio-Toledo
Applied General Topology  vol: 13  issue: 1  year: 2013  
doi: 10.4995/agt.2012.1634



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Universitat Politècnica de València

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