Remarks on finite topological spaces

Remarks on soft topological spaces

The purpose of this paper is to study soft sets and soft topological spaces. We also introduce the concepts of soft interior point, soft interior, soft neighborhood, soft continuity and soft compactness. The relationships between soft topology and fuzzy topology are also provided. Also, some basic properties of these concepts are explored. 2010 AMS Classification: 06D72, 54A40

Remarks on Finite Subset Spaces

This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex X including their connectivity and manifold structure. It also discusses the inclusion of the singletons into the threefold subset space and shows that this subspace is weakly contractible but generally non-contractible unless X is a cogroup. Some homological calculati...

Finite Topological Spaces

(1) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i < len f holds πi f πi+1 f : Let i, j be natural numbers. If i j and 1 i and j len f ; then πi f π j f : (2) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i< len f holds πi f πi+1 f : Let i, j be natu...

Finite Topological Spaces

Remarks on g̃α-Closed Sets in Topological spaces

In this paper we introduce a new class of sets called g̃αclosed sets in topological space. We prove that this class lies between αclosed sets and gα-closed sets.We discuss some basic properties of g̃αclosed sets. Applying this we introduce a new space called T gαspace. Mathematics Subject Classification: 54C08