Proximity structure on generalized topological spaces
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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 Classification54A05 54E05
The authors are thankful to the referee for certain comments towards the improvement of the paper.