Results 241 to 250 of about 1,127,269 (277)

Uniform Continuity of Continuous Functions on Uniform Spaces

Canadian Journal of Mathematics, 1961
Recently several topologists have called attention to the uniform structures (in most cases, the coarsest ones) under which every continuous real function is uniformly continuous (let us call the structures the [coarsest] uc-structures), and some important results have been found which closely relate, explicitly or implicitly, to the uc-structures ...
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Uniform and holder continuity

Lecture Notes in Mathematics, 1978
exaly   +2 more sources

A Constructive Uniform Continuity Theorem

The Quarterly Journal of Mathematics, 2002
The celebrated uniform continuity theorem of classical mathematics states that a pointwise continuous function with metric domain is uniformly continuous if that domain is compact (which, for the purposes of constructive mathematics, is taken to mean totally bounded and complete).
Ishihara, Hajime, Schuster, Peter
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Strong continuity implies uniform sequential continuity

Archive for Mathematical Logic, 2005
This paper is a contribution to a productive and long-term project, initiated by Bridges and Vîţǎ, which aims to develop constructive topology based on the classical theory of nearness spaces. Constructively, apartness seems to be a more basic notion than nearness. In the present paper the notion of `strong continuity' is investigated.
Douglas S. Bridges, Hajime Ishihara, Peter Schuster 0001, Luminita Vîta   +3 more
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Uniform Continuity of Multifunctions

Set-Valued and Variational Analysis
Uniform continuity is investigated in the framework of multifunctions acting between metric spaces. Various characterizations of uniform continuity of set valued functions (including uniformity with respect to Hausdorff metric) are presented and illustrated by simple counterexamples.
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On Continuous Functions in Uniform Spaces

The Annals of Mathematics, 1947
It is known that if a metric space E is compact, every (real) continuous function reaches its upper bound, and conversely, if in a metric space E every continuous function reaches its upper bound then E is compact.' The uniform spaces2 being the "modern substitute for metric spaces" we shall try to extend to them the above mentioned result.
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Examining Continuity and Uniform Continuity of Functions

2020
One of the fundamental notions in topology is that of the continuity of functions, which constitutes our concern in this chapter.
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The Fan Theorem and Uniform Continuity

2005
In presence of continuous choice the fan theorem is equivalent to each pointwise continuous function f from the Cantor space to the natural numbers being uniformly continuous. We investigate whether we can prove this equivalence without the use of continuous choice.
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Uniform Continuity

2020
John D. Ross, Kendall C. Richards
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Uniform Continuity of Continuous Functions on Compact Metric Spaces

The American Mathematical Monthly, 2015
A basic theorem asserts that a continuous function on a compact metric space with values in another metric space is uniformly continuous. The usual proofs based on a contradiction argument involving sequences or on the covering property of compact sets are quite sophisticated for students taking a first course on real analysis.
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