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- W3203275090 abstract "A space X is called functionally countable if ƒ (X) is countable for any continuous function ƒ : X → Ø. Given an infinite cardinal k, we prove that a compact scattered space K with d(K) > k must have a convergent k + -sequence. This result implies that a Corson compact space K is countable if the space (K × K) Δ K is functionally countable; here Δ K = {(x, x): x ϵ K} is the diagonal of K. We also establish that, under Jensen’s Axiom ♦, there exists a compact hereditarily separable non-metrizable compact space X such that (X × X) Δ X is functionally countable and show in ZFC that there exists a non-separable σ-compact space X such that (X × X) Δ X is functionally countable." @default.
- W3203275090 created "2021-10-11" @default.
- W3203275090 creator A5006813344 @default.
- W3203275090 date "2021-09-27" @default.
- W3203275090 modified "2023-10-18" @default.
- W3203275090 title "A Corson Compact Space is Countable if the Complement of its Diagonal is Functionally Countable" @default.
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- W3203275090 doi "https://doi.org/10.1556/012.2021.58.3.1508" @default.
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