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Afrika Matematika

, Volume 30, Issue 1–2, pp 91–100 | Cite as

Proximity structure on generalized topological spaces

  • M. N. Mukherjee
  • D. MandalEmail author
  • Dipankar Dey
Article
  • 89 Downloads

Abstract

The aim of the present article is to introduce a kind of proximity structure, termed \(\mu \)-proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of \(\mu \)-proximity is given and it is shown that any generalized topology of a generalized topological space \((X, \mu )\) is always induced by a suitable \(\mu \)-proximity if and only if \((X, \mu )\) satisfies a type of complete regularity condition. The notion of quasi \(\mu \)-proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi \(\mu \)-proximity, is proved.

Keywords

\(\mu \)-Proximity \(\mu \)-Complete regularity Quasi \(\mu \)-proximity 

Mathematics Subject Classification

54A05 54E05 

Notes

Acknowledgements

The authors are thankful to the referee for certain comments towards the improvement of the paper.

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia

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