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Generation of the uniformly continuous functions

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Garrido, M. Isabel and Montalvo, Francisco (2004) Generation of the uniformly continuous functions. Topology and its Applications, 137 (1-3). pp. 167-174. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864103002062


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Abstract

Let X be a set and F a family of real-valued functions on X. We denote by μFX the space X endowed with the weak uniformity given by F. In this paper we provide a method of generating the set U(μFX), of all uniformly continuous real functions on μFX, by means of the family F. In order to do that we need to study the uniform approximation of real uniformly continuous functions on subsets of Rn. As a consequence, we give an internal condition on F in order to be uniformly dense in U(μFX).


Item Type:Article
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IV Iberoamerican Conference on Topology and its Applications

Uncontrolled Keywords:Uniform spaces; Uniform density
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Topology
ID Code:21377
Deposited On:14 May 2013 15:46
Last Modified:12 Dec 2018 15:13

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