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Almost Perfectly Continuous Functions
Quaestiones Mathematicae, 2010 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 Real Functions [PDF]
Proceedings of the American Mathematical Society, 1972 A blocking set of a function f is a closed set which does not intersect f but which intersects each continuous function with domain the same as f . It is shown that for each function which is not almost continuous,
Kellum, K. R., Garrett, B. D.
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Every Almost Continuous Function Is Polygonally Almost Continuous
Real Analysis Exchange, 1999 A function \(f: \mathbb{I} \rightarrow \mathbb{R}\) is almost continuous (AC) if whenever \(U\subset \mathbb{I} \times \mathbb{R}\) is an open set containing the graph of \(f\), then \(U\) contains the graph of a continuous function. A function \(f: \mathbb{I} \rightarrow \mathbb{R}\) is polygonally almost continuous (PAC) if whenever \(U\subset ...
Piotr Szuca
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Continuous Mappings of Almost Automorphic and Almost Periodic Functions^(*) [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1964 S Bochner
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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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Measurable Functions and Almost Continuous Functions
Manuscripta Mathematica, 1981 I show that if (X, μ) is a Radon measure space and Y is a metric space, then a function from X to Y is μ-measurable iff it is almost continuous (=Lusin measurable). I discuss other cases in which measurable functions are almost continuous.
D H Fremlin
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On Almost β-Continuous Functions
Acta Mathematica Hungarica, 1998A subset \(A\) of a topological space \(X\) is called \(\beta\)-open if \(A\subset \text{Cl}(\text{Int}(\text{Cl}(A)))\). A function \(f:X\to Y\) is called almost \(\beta\)-continuous at \(x\in X\) if for every open neighbourhood \(V\) of \(f(x)\) there exists a \(\beta\)-open set \(U\) containing \(x\) such that \(f(U)\subset \text{Int} (\text{Cl}(V))\
Noiri, T., Popa, V.
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