This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the property of being close to uniformly continuous.

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UNIFORM GENERALIZED ABSOLUTE CONTINUITY

Bongiorno · Real Analysis Exchange · 1993

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Real Function Uniform Continuity

Jarosław Kotowicz, Konrad Raczkowski · 1990

Summary. The uniform continuity for real functions is introduced. More theorems concerning continuous functions are given. (See [10]) The Darboux Theorem is exposed. Algebraic features for uniformly continuous functions are presented. Various facts, e.g., a continuous function on a compact set is uniformly continuous are proved.

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Uniform continuity of POVMs

Beneduci, Roberto · arXiv (Cornell University) · 2013

Recently a characterization of uniformly continuous POVMs and a necessary condition for a uniformly continuous POVM $F$ to have the norm-1 property have been provided. Moreover it was proved that in the commutative case, uniform continuity corresponds to the existence of a Feller Markov kernel. We apply such results to the analysis of some relevant physical examples; i.e., the phase space localization observables, the unsharp phase observable and the unsharp number observable of which we study the uniform continuity, the norm-1 property and the existence of a Feller Markov kernel.

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Strong and Uniform Continuity – the Uniform Space Case

Douglas Bridges, Luminiţa Vı̂ţă · LMS Journal of Computation and Mathematics · 2003

Abstract It is proved, within the constructive theory of apartness spaces, that a strongly continuous mapping from a totally bounded uniform space with a countable base of entourages to a uniform space is uniformly continuous. This lifts a result of Ishihara and Schuster from metric to uniform apartness spaces. The paper is part of a systematic development of computable topology using apartness as the fundamental notion.

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Real Function Uniform Continuity 1

Université Catholique De Louvain, Konrad Raczkowski · 2008

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