A reverse viewpoint on the upper semicontinuity of multivalued maps

Marcio Colombo Fenille

Displaying similar documents to “A reverse viewpoint on the upper semicontinuity of multivalued maps”

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

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For a space $Z$ , we denote by $ℱ (Z)$ , $𝒦 (Z)$ and $ℱ_{2} (Z)$ the hyperspaces of non-empty closed, compact, and subsets of cardinality $\leq 2$ of $Z$ , respectively, with their Vietoris topology. For spaces $X$ and $E$ , $C_{p} (X, E)$ is the space of continuous functions from $X$ to $E$ with its pointwise convergence topology. We analyze in this article when $ℱ (Z)$ , $𝒦 (Z)$ and $ℱ_{2} (Z)$ have continuous selections for a space $Z$ of the form $C_{p} (X, E)$ , where $X$ is zero-dimensional and $E$ is a strongly zero-dimensional metrizable space. We prove that $C_{p} (X, E)$ is weakly orderable...

On hit-and-miss hyperspace topologies

Gerald Beer, Robert K. Tamaki (1993)

Commentationes Mathematicae Universitatis Carolinae

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The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family $Δ$ of closed sets. In the case of the Fell topology, where $Δ$ consists of the compact sets, a closed set $A$ misses a member $B$ of $Δ$ if and only if $A$ is far from $B$ in a uniform...

Positive solutions for systems of generalized three-point nonlinear boundary value problems

Johnny Henderson, Sotiris K. Ntouyas, Ioannis K. Purnaras (2008)

Commentationes Mathematicae Universitatis Carolinae

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Values of $λ$ are determined for which there exist positive solutions of the system of three-point boundary value problems, $u^{''} + λ a (t) f (v) = 0$ , $v^{''} + λ b (t) g (u) = 0$ , for $0 < t < 1$ , and satisfying, $u (0) = β u (η)$ , $u (1) = α u (η)$ , $v (0) = β v (η)$ , $v (1) = α v (η)$ . A Guo-Krasnosel’skii fixed point theorem is applied.