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Transactions of the American Mathematical Society

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

 

 

Separation and coding


Author: Stephen Watson
Journal: Trans. Amer. Math. Soc. 342 (1994), 83-106
MSC: Primary 54D15; Secondary 54E30, 54G15, 54G20
DOI: https://doi.org/10.1090/S0002-9947-1994-1225576-8
MathSciNet review: 1225576
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Abstract: We construct a normal collectionwise Hausdorff space which is not collectionwise normal with respect to copies of [0,1]. We do this by developing a general theory of coding properties into topological spaces. We construct a para-Lindelöf regular space in which para-Lindelöf is coded directly rather than $ \sigma $-para-Lindelöf and normal. We construct a normal collectionwise Hausdorff space which is not collectionwise normal in which collectionwise Hausdorff is coded directly rather than obtained as a side-effect to countable approximation. We also show that the Martin's axiom example of a normal space which is not collectionwise Hausdorff is really just a kind of "dual" of Bing's space.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1225576-8
Article copyright: © Copyright 1994 American Mathematical Society