Extending maps between 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.2012.1634
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Keywords:

Minimal, Round, Pre-uniform, Completion, Extension

Supporting agencies:

This research was not funded

Abstract:

We give sufficient conditions on a uniformly continuous map f: (X,U) → (Y, V ) between completable T1-pre-uniform spaces (X,U), (Y, V ) to have a continuous or a uniformly continuous extension f:X → Y between the corresponding completions.
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References:

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

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

D. Harris, Structures in Topology, Memoirs of The American Mathematical Society, No. 115, Providence, Rhode Island, AMS, 1971.

R. Mancio Toledo, Los espacios pre-uniformes y sus completaciones, Ph. D. Thesis, UNAM, 2006.

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