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. |