Extension of continuous functions into uniform spaces
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- by Salvador Hernández PDF
- Proc. Amer. Math. Soc. 97 (1986), 355-360 Request permission
Abstract:
Let $X$ be a dense subspace of a topological space $T$, let $Y$ be a uniformizable space, and let $f:X \to Y$ a continuous map. In this paper we study the problem of the existence of a continuous extension of $f$ to the space $T$. Thus we generalize basic results of Taimanov, Engelking and Blefko-Mrówka on extension of continuous functions. As a consequence, if $\mathcal {D}$ is a nest generated intersection ring on $X$, we obtain a necessary and sufficient condition for the existence of a continuous extension to $v (X,\mathcal {D})$, of a continuous function over $X$, when the range of the map is a uniformizable space, and we apply this to realcompact spaces. Finally, we suppose each point of $T\backslash X$ has a countable neighbourhood base, and we obtain a generalization of a theorem by Blair, herewith giving a solution to a question proposed by Blair.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 355-360
- MSC: Primary 54C20; Secondary 54C30, 54D60
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835898-9
- MathSciNet review: 835898