GENERALIZATION OF SIERPIŃSKI SPACE
Kamran Alam Khan · Research journal of pure algebra · 2012
In 1994, F. J. Craveiro de carvalho and D’Azevedo Breda took up the task of generalizing the Sierpinski space and introduced the concept of locally Sierpinski space ([4]). In this paper, we choose a different approach and propose a generalization of Sierpinski space by defining a topology analogous to Sierpinski topology with nested open sets on any arbitrary non-empty set. We then introduce the notion of Special finite generalized Sierpinski space as a special case of generalized Sierpinski space. We investigate some of the properties of the generalized Sierpinski spaces and obtained a formula for the number of finite generalized Sierpinski topologies using Stirling number of the second kind. Finally we show that every special finite generalized Sierpinski space is a D-space.