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Unions of chains in dyadic compact spaces and topological groups. (English) Zbl 1009.54007
This paper explores properties possessed by a space \(X\) which is a union of a chain \(\{ X_\alpha\mid \alpha <\kappa\}\) of subspaces each of which has some bounded cardinal function. For example if \(X\) is a dyadic compactum and either each \(X_\alpha\) has pseudocharacter at most \(\lambda\) or each \(X_\alpha\) has tightness at most \(\lambda\) then \(X\) has weight at most \(\lambda\). Similar assumptions for a locally compact group give a corresponding bound on the character of the group.

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54H11 Topological groups (topological aspects)
54B10 Product spaces in general topology
54D30 Compactness
54D45 Local compactness, \(\sigma\)-compactness
22D05 General properties and structure of locally compact groups
Full Text: DOI
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