Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 22, No. 3, pp. 285-304 (2006)

New approach for closure spaces by relations

A. A. Allam, M. Y. Bakeir, E. A. Abo-Tabl

Assuit University

Abstract: Recently, the general topology has become the appropriated frame for every collection related to relations because topology is required not only for mathematics and physics but also for biology, rough set theory, biochemistry, and dynamics. In this paper, we have introduced another concept of the closure operator. In so doing, the idempotent condition, which has never been realized, is achieved. The topologies associated with these closure operators are studied. And we study the subspace, continuous functions and lower separation axioms in this space. Also we study these space in digital topology.

Keywords: Closure space, minimal neighborhood, closure subspace, continuous functions, lower separation axioms, digital line.

Classification (MSC2000): 54A05; 54B05, 54C05, 54C10, 54D10

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