Almost e∗ -continuous functions and their characterizations

Abstract

The main goal of this paper is to introduce and investigate a new class of functions called almost e * -continuous functions containing the class of almost e-continuous functions defined byÖzkoç and Kına. Several characterizations concerning almost e * -continuous functions are obtained. Furthermore, we investigate the relationships between almost e * -continuous functions and separation axioms and almost e * -closedness of graphs of functions. c 2016 all rights reserved.

On Some Functions Related to e*-θ-open Sets

“…. × X n has property P e * θ [5] if Proof Let A ∈ qe * θC(X). Suppose that F ⊆ e * -cl θ (A)/A, where ∅ ≠ F ∈ e * θC(X).…”

“…(1) e * θ -closed [3] (resp. pre e * θ -closed [5]), if the image of each closed (resp. e *θ -closed) set…”

“…In 2015, Farhan and Yang [10] Again within the same year, Ayhan and Özkoç [5] defined and studied pre e * θ -open functions. In 2022, Ayhan [4] introduced and investigated weakly e * θ -open functions and also obtained some characterizations of its.…”

On Weakly e*-θ-open Functions and Their Characterizations

“…(i) weakly a-continuous (briefly w.a.c.) [5] if for all x ∈ X and all open set V of Y containing f (x), there exists U ∈ aO(X, x) such that f [U ] ⊆ cl(V ). (j) weakly e-continuous (briefly w.e.c.)…”