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A homogeneous space of point-countable but not of countable type

Désirée Basile, Jan van Mill (2007)

Commentationes Mathematicae Universitatis Carolinae

We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.

Applications of maximal μ-open sets in generalized topology and quasi topology

Bishwambhar Roy, Ritu Sen (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, some fundamental properties of maximal μ-open sets such as decomposition theorem for a maximal μ-open set, are given in a generalized topological space. Some basic properties of intersection of maximal μ-open sets are established, cohere the law of μ-radical μ-closure in a quasi topological space is obtained, among the other things.

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