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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the extension of mappings in Stone-Weierstrass spaces


Author: Anthony J. D’Aristotle
Journal: Trans. Amer. Math. Soc. 208 (1975), 91-101
MSC: Primary 54C20
DOI: https://doi.org/10.1090/S0002-9947-1975-0385790-9
MathSciNet review: 0385790
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Abstract: N. Veličko generalized the well-known result of A. D. Taĭmanov on the extension of continuous functions by showing that Taĭmanov's theorem holds when $ Y$ (the image space) is $ H$-closed and Urysohn and the mapping $ f$ is weakly $ \theta $-continuous. We obtain, in a more direct fashion, an even stronger generalization of this theorem.

We proceed to show that the class of all SW spaces is not reflective in the category of all completely Hausdorff spaces and continuous mappings. However, an epi-reflective situation is achieved by suitably enlarging the class of admissible morphisms.

We conclude by establishing a number of results about SW extension spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0385790-9
Article copyright: © Copyright 1975 American Mathematical Society