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Almost Perfectly Continuous Functions
The aim of the present paper is to continue the study of almost perfectly continuous (≡ regular set connected) functions initiated by Dontchev, Ganster and Reilly. It turns out that in general the notion of almost perfectly continuity is independent of continuity but represents a significantly strong form of continuity called ‘cl-supercontinuity’, if Y
Singh, D
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Almost Continuous Functions with Closed Graphs
AbstractA function f:X → Y is almost continuous if for every x ∊ X and for each open set V ⊂ Y containing f(x), Cl(f-l(V)) is a neighborhood of x. Various conditions are given that guarantee that an almost continuous function is continuous. The main theorem states that if f:X → Y is almost continuous with a closed graph (closed in X × Y) and X and Y ...
Andrew J. Berner
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Keskin, Aynur, Noiri, Takashi
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A Characterization of Real almost Continuous Functions
The main purpose of this note is to give a characterization of almost continuous functions similar to that of approximately continuous functions ([3], §235, p. 312). The characterization of approximately continuous real functions has been used to show that each approximately continuous function is almost continuous ([4], §6).
Husain, T., Dwivedi, T. D.
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A note on almost β-continuous functions [PDF]
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Ekici, Erdal
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On Approximately Continuous and Almost Continuous Functions
Canadian Mathematical Bulletin, 1971The purpose of this note is to discuss the relationship between the concepts of approximate continuity and almost continuity of real functions of a real variable.Contrary to the papers of T. Husain [1], [2], [3], we shall show that there is little relationship between these concepts, that approximate continuity does not imply almost continuity without ...
Chaika, M., Perlman, S.
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