Dual uniformities in function spaces over uniform continuity

The notion of dual uniformity is introduced on , the uniform space of uniformly continuous mappings between and , where and are two uniform spaces. It is shown that a function space uniformity on is admissible (resp. splitting) if and only if its dual uniformity on is admissible (resp. splitting). I...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2022-12, Vol.20 (1), p.1926-1936
Main Authors: Gupta, Ankit, Sarma, Ratna Dev, Alshammari, Fahad Sameer, George, Reny
Format: Article
Language:English
Subjects:
54A20
54C35
admissibility
Continuity (mathematics)
dual uniformity
Function space
Splitting
splittingness
uniform space
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Summary:The notion of dual uniformity is introduced on , the uniform space of uniformly continuous mappings between and , where and are two uniform spaces. It is shown that a function space uniformity on is admissible (resp. splitting) if and only if its dual uniformity on is admissible (resp. splitting). It is also shown that a uniformity on is admissible (resp. splitting) if and only if its dual uniformity on is admissible (resp. splitting). Using duality theorems, it is also proved that the greatest splitting uniformity and the greatest splitting family open uniformity exist on and , respectively, and these two uniformities are mutually dual splitting uniformities.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2022-0505