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Camillo Costantini 9A= H@AH=>EEJO B IA IF=?AI MDE?D =@EJ = MA= IAA? JE

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Camillo Costantini

Weak orderability of some spaces which admit a weak selec- tion

Comment.Math.Univ.Carolin. 47,4 (2006) 609-615.

Abstract: We show that if a Hausdorff topological spaceX satisfies one of the following properties:

a) X has a countable, discrete dense subset andX2 is hereditarily collectionwise Hausdorff;

b)X has a discrete dense subset and admits a countable base;

then the existence of a (continuous) weak selection onX 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.

Keywords: weak (continuous) selection, weak orderability, Vietoris topology, dense countable subset, isolated point, countable base, collectionwise Hausdorff space AMS Subject Classification: Primary 54C65, 54F05; Secondary 54D15, 54D70, 54E35

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