Generalization of Homeomorphisms


Keywords:
$sg\alpha$-open sets, $sg\alpha$-continuous functions, $sg\alpha$-irresolute functions, $sg\alpha^*$-homeomorphismsAbstract
In this paper, we first introduce a new class of closed functions called $sg\alpha$-closed functions also introduce a new class of homeomorphisms called $sg\alpha^*$-homeomorphisms, which are weaker than homeomorphisms. We also prove that the set of all $sg\alpha^*$-homeomorphisms forms a group under the operation composition of functions.
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