Left separated spaces with point-countable bases

Author:

Fleissner William G.

Abstract

Theorem 2.2 lists properties equivalent to left separated spaces in the class of T 1 {T_1} with point-countable bases, with examples preventing plausible additions to this list. For example, X X is left iff X X is σ \sigma -weakly separated or X X has a closure preserving cover by countable closed sets, but X X is left separated does not imply that X X is σ \sigma -discrete. Theorem 2.2 is used to show that the following reflection property holds after properly collapsing a supercompact cardinal to ω 2 {\omega _2} : If X X is a not σ \sigma -discrete metric space, then X X has a not σ \sigma -discrete subspace of cardinality less than ω 2 {\omega _2} . Similar reflection properties are shown true in some models and false in others.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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