Separation and coding

Watson, Stephen

doi:10.1090/S0002-9947-1994-1225576-8

Separation and coding
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Trans. Amer. Math. Soc. 342 (1994), 83-106 Request permission

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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Combinatorial set theory