Strongly Connectedness in Closure Space

Abstract

A Cech closure space (X, u) is a set X with Cech closure operator u: P(X) → P(X) where P(X) is a power set of X, which satisfies u ф=ф, A ⊆uA for every A⊆X, u (A⋃B) = uA⋃uB, for all A, B ⊆ X. Many properties which hold in topological space hold in closure space as well. A topological space X is strongly connected if and only if it is not a disjoint union of countably many but more than one closed set. If X is strongly connected, and Ei"s are nonempty disjoint closed subsets of X, then X≠ E1⋃E2⋃. We further extend the concept of strongly connectedness in closure space. The aim of this paper is to introduce and study the concept of strongly connectedness in closure space.