Journal Name:
- European Journal of Pure and Applied Mathematics
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Abstract (2. Language):
A subset A of topological space (X, ) is said to be ! −open [3] if for every x ∈ A there
exists an −open set U containing x such that U − A is a countable. In this paper, we introduce and
study new class of function which is ! −continuous functions by using the notion of ! −open sets.
This new class of function defines as a function f : (X, )→(Y,) from a topological space (X, ) into
a topological space (Y,) is ! −Continuous function if and only if for each x ∈ X and each open set
V in (Y,) containing f (x) there exists an ! −open set U containing x such that f (U) ⊆ V. We give
some characterizations of ! −Continuous functions, define ! −irresolute and ! −open function.
Finally, we find relationship between these type of function.
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FULL TEXT (PDF):
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129-140