A study of uniformities on the space of uniformly continuous mappings

Ankit Gupta; Abdulkareem Saleh Hamarsheh; Ratna Dev Sarma; Reny George

doi:10.1515/math-2020-0110

A study of uniformities on the space of uniformly continuous mappings

Ankit Gupta, Abdulkareem Saleh Hamarsheh, Ratna Dev Sarma, Reny George

Mathematics

University of Delhi

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

New families of uniformities are introduced on U C (X, Y) UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X, U) and (Y, V) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.

Original language	English
Pages (from-to)	1478-1490
Number of pages	13
Journal	Open Mathematics
Volume	18
Issue number	1
DOIs	https://doi.org/10.1515/math-2020-0110
State	Published - 1 Jan 2020

Keywords

admissibility
function space
splittingness
uniform space
uniformly continuous mappings

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abstract = "New families of uniformities are introduced on U C (X, Y) UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X, U) and (Y, V) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.",

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KW - function space

KW - splittingness

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KW - uniformly continuous mappings

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A study of uniformities on the space of uniformly continuous mappings

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Keywords

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