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On the “Essential Metrization” of Uniform Spaces

Published online by Cambridge University Press:  20 November 2018

Elias Zakon
Elias Zakon*
Affiliation:
University of Windsor, Canada, Summer Research Institute of the Canadian Mathematical Congress
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The notion of “essential metrization” was introduced in (8) where it was used to obtain some extensions of the theorems of Egoroff and Lusin on measurable functions. In the present note we shall further develop the theory of essential metrization, in its own right.

As is well known, sets of measure zero (“null sets“) may be disregarded in many problems of measure theory. Hence the usual topological prerequisites of such problems are actually too restrictive and may be replaced by what could be called “topology modulo null-sets,” imitating such notions as “approximate continuity,” “essential supremum,” etc. Thus we consider spaces in which certain topological properties (such as metrizability, separability, etc.) hold not in the usual sense but only “essentially,” i.e. to within some null sets, as defined below.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1224 - 1236
Copyright
Copyright © Canadian Mathematical Society 1966

References

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