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Proximity structure on generalized topological spaces
M N MUKHERJEE, , D DEY
Published in Springer Verlag
2019
Volume: 30
   
Issue: 43467
Pages: 91 - 100
Abstract
The aim of the present article is to introduce a kind of proximity structure, termed μ-proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of μ-proximity is given and it is shown that any generalized topology of a generalized topological space (X, μ) is always induced by a suitable μ-proximity if and only if (X, μ) satisfies a type of complete regularity condition. The notion of quasi μ-proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi μ-proximity, is proved. © 2018, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.
About the journal
JournalData powered by TypesetAfrika Matematika
PublisherData powered by TypesetSpringer Verlag
ISSN1012-9405
Open AccessNo