On (τi,τj)-gsh-closed sets, SH (τi,τj)-σkσkcontinuous functions and Tgsh-spaces in bitopological spaces

Muhammad Ameen Hussain, Wuria

	On (τi,τj)-gsh-closed sets, SH (τi,τj)-σkσkcontinuous functions and Tgsh-spaces in bitopological spaces
Al-Mustansiriyah Journal of Science
Article 1, Volume 17, Issue 2, 2006, Pages 60-73
Author
Wuria Muhammad Ameen Hussain
Abstract
In this paper, we define a new types to the best of our knowledge of generalized closed sets called (τi, τj)-gsh-closed and generalized continuous functions called SH (τi, τj)-σk-continuous in BS, also we define a separation axiom (τi, τj)-Tgsh-space in BS. Some of their properties with other concepts in BS have been studied in the following: - 1- (τi, τj)-gsh-closed sets is weaker than (τi, τj)-wg-closed sets. 2- For any BS (X,τ1, τ2), if τj = τi βC (X)τ, then every subsets of X is pairwise-gsh-closed set. 3- For any BS (X,τ1, τ2), either {x} is (τi, τj)-gsh-closed or {x} c is (τj, τi)-gshclosed set. 4- If a BS (X,τ1, τ2) is pairwise R0-space, then every singleton is pairwise gsh-closed set. 5- Each W (τi, τj)- σk-continuous function is SH (τi, τj)- σkcontinuous. 6- Every pairwise β-continuous function f: (X, τ1, τ2)→(Y, σ1,σ2) is gsh-bicontinuous. 7- If a BS (X,τ1, τ2) is (τi, τj)-Tgsh-space, then it is (τi, τj)-Twg-space. 8- The converse of the results (4-) and (6-) is true if (X, τ1, τ2) is strongly pairwise Tgsh-space.

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