Displaying similar documents to “On tho existence of weak P-points in compact F-spaces”

Weak orderability of some spaces which admit a weak selection

Camillo Costantini (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if a Hausdorff topological space X satisfies one of the following properties: a) X has a countable, discrete dense subset and X 2 is hereditarily collectionwise Hausdorff; b) X has a discrete dense subset and admits a countable base; then the existence of a (continuous) weak selection on X implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.