Strongly Connectedness in Closure Space

Tapi, U.D.; Deole, Bhagyashri A.

doi:10.18052/www.scipress.com/BMSA.9.69

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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:

August 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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Open Access

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Creative Commons Attribution 4.0 International License

References:

Čech E. (1968) Topological space,. Topological Papers of Eduard Čech , Academia, Prague, 436-472.

Boonpok C. (2009)On continuous maps in closure spaces,. General Mathematics Vol. 17, No. 2, 127-134.

Dai Bo. and Yan-loi. Wong. (2000) Strongly connected spaces". Department of Mathematics, National University of Singapore.

Eissa D. Habil, Khalid A. Elzenati (2006) Connectedness in Isotonic spaces,. Turk J. Math Tubitak, 247-262, 30.

Eissa D. Habil(2006)Hereditary properties in isotonic spaces,. Department of Mathematics, Islamic University of Gaza P.O. Box 108, Gaza, Palestine.

Stadler .M.R. and Stadler P.F. (2002), asic properties of closure spaces., J. Chem. Inf. Computer. Sci. 42, p: 577.

Riesz F., Stetigkeitsbegriff(1909) und Abstrakte Mengenlehre, in Atti del IV Congress. Internationale di Mat., II, pp.18-24.

Tapi U.D. and Deole hagyashri A. (July, 2013) Connectedness in closure space,. International journal of Math. Sci. & Eng. Appls. (IJMSEA), Vol. 7, No. 4, pp.147-150.

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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