Finite and countable additivity of topological properties in nice spaces
V. V. Tkachuk
Trans. Amer. Math. Soc. 341 (1994), 585-601
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Abstract: Let character , pseudocharacter , tightness , weight , -property, discreteness, Fréchet-Urysohn property, sequentiality, radiality, pseudoradiality, local compactness, -property. If , for all then (i.e. the property is -additive in for any ). Metrizability is -additive in provided is compact or . -property is closely -additive in if is compact ("closely" means additivity in case is closed in ). If metrizability, character , pseudocharacter , diagonal number , -weight , pseudoweight , local compactness then is finitely additive in any topological group.
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