Abstract
A Čech closure space (X, u) is a set X with Čech closure operator u: P(X) → P(X) where P(X) is a power set of X, which satisfies u𝝓=𝝓, 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.
Highlights
Čech closure space was introduced by Čech E. [1] in 1963
The modern notion of connectedness was proposed by Jorden (1893) and Schoenfliesz, and put on firm footing by Riesz [7] with the use of subspace topology
We introduce strongly connectedness in closure space and study some of their properties
Summary
Čech closure space was introduced by Čech E. The modern notion of connectedness was proposed by Jorden (1893) and Schoenfliesz, and put on firm footing by Riesz [7] with the use of subspace topology. Many mathematicians such as EissaD.Habil, Khalid A. Habil [5], Stadler B.M.R. and Stadler P.F. [6] have extended various concepts of strongly connectedness in topological space. We introduce strongly connectedness in closure space and study some of their properties
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