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A denumerable cellular family of a topological space is a countably infinite collection of pairwise disjoint non-empty open sets of . is the sentence: For every infinite set , the set of all finite subsets of has a countably infinite subset. Among other results, the following are proved in : (i) iff every infinite 0-dimensional Hausdorff space admits a denumerable cellular family; (ii) implies that every infinite Hausdorff Baire space has a denumerable cellular family; (iii) if every metrizable Cantor cube is pseudocompact, then every non-empty countable collection of non-empty finite sets has a choice function; (iv) all metrizable Cantor cubes are paracompact; (v) the conjunction of with a new modification of the Kinna–Wagner selection principle for families of finite sets implies that every infinite Boolean algebra has a tower and every infinite Hausdorff space has a denumerable cellular family.
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Kyriakos Keremedis, Eliza Wajch, Denumerable cellular families in . Port. Math. 78 (2021), no. 3, pp. 281–321DOI 10.4171/PM/2070