Displaying similar documents to “A generalization of Thom’s transversality theorem”

A reverse viewpoint on the upper semicontinuity of multivalued maps

Marcio Colombo Fenille (2013)

Mathematica Bohemica

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For a multivalued map ϕ : Y ( X , τ ) between topological spaces, the upper semifinite topology 𝒜 ( τ ) on the power set 𝒜 ( X ) = { A X : A } is such that ϕ is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map ϕ : Y ( 𝒜 ( X ) , 𝒜 ( τ ) ) . In this paper, we seek a result like this from a reverse viewpoint, namely, given a set X and a topology Γ on 𝒜 ( X ) , we consider a natural topology ( Γ ) on X , constructed from Γ satisfying ( Γ ) = τ if Γ = 𝒜 ( τ ) , and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued...

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 ( Z ) , 𝒦 ( Z ) and 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality 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 ( Z ) , 𝒦 ( Z ) and 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...

Whitney blocks in the hyperspace of a finite graph

Alejandro Illanes (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a finite graph. Let C ( X ) be the hyperspace of all nonempty subcontinua of X and let μ : C ( X ) be a Whitney map. We prove that there exist numbers 0 < T 0 < T 1 < T 2 < < T M = μ ( X ) such that if T ( T i - 1 , T i ) , then the Whitney block μ - 1 ( T i - 1 , T i ) is homeomorphic to the product μ - 1 ( T ) × ( T i - 1 , T i ) . We also show that there exists only a finite number of topologically different Whitney levels for C ( X ) .