Extending maps between pre-uniform spaces

Adalberto García-Máynez, Rubén Mancio-Toledo

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.

Keywords

Minimal; Round; Pre-uniform; Completion; Extension

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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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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt