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- W2037401766 abstract "A topological property P is called n -additive in n th power (or weakly n -additive) if a topological space X has P as soon as X n = ∪{ Y i : i ϵ n } where all Y i have P. If P is n -additive in n th power for all natural n ⩾ 1, we say that P is weakly finitely additive. The main question we deal with in this paper is whether metrizability is weakly finitely additive. It was proved by Tkachuk (1994) that it is so in the class of regular spaces with Souslin property. Metrizability was also proved by Tkachuk (1994) to be weakly finitely additive in the class of Hausdorff compact spaces. We generalize this last result, showing that metrizability is weakly finitely additive in the class of regular pseudocompact spaces. We also prove that if X n is a regular Lindelöf space then it is metrizable if represented as a union of its n metrizable subspaces. We show that there is an example of a Tychonoff nonmetrizable space X such that X n is a union of two metrizable subspaces for all n ⩾ 1. The method of constructing this example can be used to solve several problems stated by Tkachuk (1994)." @default.
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- W2037401766 date "1998-04-01" @default.
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- W2037401766 title "Additivity of metrizability and related properties" @default.
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- W2037401766 doi "https://doi.org/10.1016/s0166-8641(97)00085-0" @default.
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