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Abstract
The main purpose of this paper is to introduce *-operfect, τ*-clopen, α-*-closed, strongly α-*-closed and pre-*-closed sets. We compare them and obtain a diagram to show their relationships among these sets and related sets.
Abstract
Let X, Y be T 1 topological spaces. A partial map from X to Y is a continuous function f whose domain is a subspace D of X and whose codomain is Y. Let P(X, Y) be the set of partial maps with domains in a fixed class D. In analogy with the global case, we introduce on P(X, Y), whatever be the nature of the domain class D, new function space topologies, the proximal set-open topologies, briefly PSOTs, deriving from general networks on X and proximity on Y by replacing inclusion with strong inclusion. The PSOTs include the already known generalized compact-open topology on partial maps with closed domains. When domains are supposed closed, the network α closed and hereditarily closed and the proximity δ on Y Efremovic, then the PSOT attached to α and δ is uniformizable iff α is a Urysohn family in X.
Associated topologies of generalized α -closed sets and α generalized closed sets Mem. Fac. Sci. Kochi Univ. (Math.) 15 51 – 63 . [24] Mashhour , A. S. , Abd El-Monsef , M. E. , El
. Balachandran , K. 1994 Associated topologies of generalized α -closed sets and α -generalized closed sets Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 15 51 – 63
