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Strongly Connectedness in Closure Space

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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.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 9)
Pages:
69-71
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.9.69
Citation:
U.D. Tapi and B. A. Deole, "Strongly Connectedness in Closure Space", Bulletin of Mathematical Sciences and Applications, Vol. 9, pp. 69-71, 2014
Online since:
Aug 2014
Authors:
U.D. Tapi, Bhagyashri A. Deole
Keywords:
Closure Space, Connected Closure Space, Connected Space, Strongly Connected Closure Space, Strongly Connected Space
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Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

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Tapi U.D. and Deole hagyashri A. z-Connectedness in closure space,. Kathmandu University Journal of Science, Engineering and Technology. (Under communication).

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