• GENERALIZATION OF SIERPIŃSKI SPACE

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.