Abstract
We introduce the notions of locally b -closed, b - t -set, b - B -set, locally b -closed continuous, b - t -continuous, b - B -continuous functions and obtain decomposition of continuity and complete continuity.
Highlights
We note that a subset A of X is locally closed if and only if A = U ∩ Cl(A) for some open set U
A subset A of a topological space X is called sb-generalized closed if s(bCl(A)) ⊆ U, whenever A ⊆ U and U is b-preopen
From the following examples we can see that α-continuous functions and locally b-closed-continuous functions are independent
Summary
We note that a subset A of X is locally closed if and only if A = U ∩ Cl(A) for some open set U (see [3]). A subset A of a topological space X is called D(c, b)-set if Int(A) = bInt(A). Let H be a subset of (X, τ ), His locally b-closed if and only if there exists an open set U ⊆ X such that H = U ∩ bCl(H) Let A be a subset a topological space X if A is locally b-closed,
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