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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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