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Weak orderability of second countable spaces

Valentin Gutev (2007)

Fundamenta Mathematicae

We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.

Weak orderability of some spaces which admit a weak selection

Camillo Costantini (2006)

Commentationes Mathematicae Universitatis Carolinae

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.

Weak selections and weak orderability of function spaces

Valentin Gutev (2010)

Czechoslovak Mathematical Journal

It is proved that for a zero-dimensional space $X$ , the function space $C_{p} (X, 2)$ has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if $X$ is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space $E$ , the function space $C_{p} (X, E)$ is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial...

Weakly smooth dendroids

Lewis Lum (1974)