• GENERALIZATION OF SIERPIŃSKI SPACE

Kamran Alam Khan*

Abstract


In 1994, F. J. Craveiro de carvalho and D’Azevedo Breda took up the task of generalizing the Sierpiński space and introduced the concept of locally Sierpiński space ([4]). In this paper, we choose a different approach and propose a generalization of Sierpiński space by defining a topology analogous to Sierpiński topology with nested open sets on any arbitrary non-empty set. We then introduce the notion of Special finite generalized Sierpiński space as a special case of generalized Sierpiński space. We investigate some of the properties of the generalized Sierpiński spaces and obtained a formula for the number of finite generalized Sierpiński topologies using Stirling number of the second kind. Finally we show that every special finite generalized Sierpiński space is a D-space.

Keywords


Sierpiński Space, Generalized Sierpiński Space, compactness, connectedness, separation axioms, D-space

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