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IV Iberoamerican Conference on Topology and its Applications (IV CITA)
April 18-21, 2001
University of Coimbra
Coimbra, Portugal

Organizers
Maria Manuel Clementino, Jorge Picado, Lurdes Sousa, Maria João Ferreira, Gonçalo Gutierres, Dirk Hofmann

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Generation of the uniformly continuous functions
by
Francisco Montalvo
Universidad de Extremadura, Badajoz
Coauthors: Isabel Garrido

Let X be a non-empty set and F be a vector lattice of real-valued functions on X containing all the constant functions. Consider X endowed with the weak uniformity given by F, and let C(X) (resp. U(X)) be the collection of the real-valued continuous (resp. uniformly continuous) functions over X. We do not know any general method of directly generating C(X) from F. However, the analogous problem of generating U(X) from F was solved by Hager in 1978. Our intention here is to contribute to the explanation of this (for us) nice problem by considering different methods of generating U(X) from F. To this aim we show that the general problem can be reduced to find a good description of the set of the uniformly continuous functions defined on a subset of Rn. In addition, we give an internal condition on F which is necessary and sufficient for F to be uniformly dense in U(X).

Date received: March 2, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-56.