Abstract. We prove that: (i) a pathwise connected, Hausdorff space which has a continuous selection is homeomorphic to one of the following four spaces: singleton, [0, 1), [0, 1] or the long line L, (ii) a locally connected (Hausdorff) space which has a continuous selection must be orderable, and (iii) an infinite connected, Hausdorff space has exactly two continuous selections if and only if it is compact and orderable. We use these results to give various characterizations of intervals via continuous selections. For instance, (iv) a topological space X is homeomorphic to [0, 1] if (and only if) X is infinite, separable, connected, Hausdorff space and has exactly two continuous selections, and (v) a topological space X is homeomorphic to [...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
AbstractGiven a relation Ω:X→Y between topological spaces, we inquire whether it has a constant sele...
We show that if a topological space X has a dense countable subset consisting of isolated points, an...
Abstract. The present paper extends the idea to characterize topological prop-erties of a space X by...
AbstractWe study properties of Hausdorff spaces X which depend on the variety of continuous selectio...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
Abstract. The present paper improves a result of [3] by showing that a space X is topologically well...
summary:We show that if a Hausdorff topological space $X$ satisfies one of the following properties:...
We study properties of Hausdorff spaces X which depend on the variety of continuous selections for t...
Abstract. Suppose that X is a Hausdor space such that its Vietoris hyper-space (F(X); V) has a cont...
AbstractWe study properties of Hausdorff spaces X which depend on the variety of continuous selectio...
The purpose of this note is proving that a locally connected space with a continuous selection is or...
AbstractLet T be a locally compact Hausdorff space and let G denote a finite-dimensional subspace of...
We study continuous selectors σ: Fτ (X) → X where Fτ (X) is a hyperspace of non-empty closed subsets...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
AbstractGiven a relation Ω:X→Y between topological spaces, we inquire whether it has a constant sele...
We show that if a topological space X has a dense countable subset consisting of isolated points, an...
Abstract. The present paper extends the idea to characterize topological prop-erties of a space X by...
AbstractWe study properties of Hausdorff spaces X which depend on the variety of continuous selectio...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
Abstract. The present paper improves a result of [3] by showing that a space X is topologically well...
summary:We show that if a Hausdorff topological space $X$ satisfies one of the following properties:...
We study properties of Hausdorff spaces X which depend on the variety of continuous selections for t...
Abstract. Suppose that X is a Hausdor space such that its Vietoris hyper-space (F(X); V) has a cont...
AbstractWe study properties of Hausdorff spaces X which depend on the variety of continuous selectio...
The purpose of this note is proving that a locally connected space with a continuous selection is or...
AbstractLet T be a locally compact Hausdorff space and let G denote a finite-dimensional subspace of...
We study continuous selectors σ: Fτ (X) → X where Fτ (X) is a hyperspace of non-empty closed subsets...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
summary:For a space $Z$, we denote by $\Cal{F}(Z)$, $\Cal{K}(Z)$ and $\Cal{F}_2(Z)$ the hyperspaces ...
AbstractGiven a relation Ω:X→Y between topological spaces, we inquire whether it has a constant sele...
We show that if a topological space X has a dense countable subset consisting of isolated points, an...