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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.

MSC:
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
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