Results 71 to 80 of about 100 (90)

The Wijsman and Attouch-Wets topologies on hyperspaces revisited

Topology and Its Applications, 1996
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R Lowen, M Sioen
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Wijsman topology on function spaces

Rendiconti Del Circolo Matematico Di Palermo, 1997
Let \(X\) and \(Y\) be metric spaces and let \(X\times Y\) be assigned the product box metric. Let each continuous function on \(X\) to \(Y\) be identified with its graph, a subset of \(X\times Y\). The authors study on the space of continuous functions, the topology induced on their graphs, by the Wijsman hyperspace topology on \(\text{CL} (X\times Y)\
Ľubica Holá
exaly   +3 more sources

Hyperspaces of separable Banach spaces with the Wijsman topology

Topology and Its Applications, 2005
Let \(\text{Cld}(X)\) be the set of all non-empty closed sets in a topological space \(X\). Let \(X= (X,d)\) be a metric space, for each \(x\in X\) and \(r> 0\), let \[ U^-(x,r)= \{A\in \text{Cld}(X): d(x,A)< r\};\;U^+(x,r)= \{A\in\text{Cld}(X): d(x,A)> r\}. \] The Wijsman topology on \(\text{Cld}(X)\) is the topology induced by the family \(\{U^-(x,r),
Wieslaw Kubis, Katsuro Sakai
exaly   +2 more sources

Wijsman and Hit-and-Miss Topologies of Quasi-Metric Spaces

Set-Valued Analysis, 2003
The authors study the relationship between the Wijsman topology and (proximal) hit-and-miss topologies on hyperspaces of quasi-metric spaces. They establish the equivalence of these hypertopologies in terms of Urysohn families of sets. They also show that for quasi-metric spaces \((X,d)\), the Hausdorff extended quasi-pseudo-metric is compatible with ...
Rodríguez-López, Jesús, Romaguera, Salvador   +1 more
openaire   +2 more sources

Every Wijsman Topology Relative to a Polish Space is Polish [PDF]

Proceedings of the American Mathematical Society, 1995
Generalizing a result of G. Beer and a result of E. Effros, we show that if ( X, d ) is a separable and completely metrizable metric space, then the hyperspace of X endowed with the Wijsman topology is separable and completely metrizable.
exaly   +3 more sources

6 Hit-And-Far-Miss Topology: A Generalization of the Wijsman Topology

2009
exaly   +2 more sources

Coincidence of Vietoris and Wijsman topologies: A new proof

2009
Summary: Let \((X,d)\) be a metric space and \(\text{CL}(X)\) the family of all nonempty closed subsets of \(X\). We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric \(d\) forces \(X\) to be a compact space.
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Norms that generate the same Wijsman topology on convex sets

1995
Summary: In a Banach space \(X\), we introduce a criterion for comparing the Wijsman topologies that are induced by two equivalent norms of \(X\) on the hyperspace of closed convex sets \(C(X)\). Thereafter, we study the duality map associated with the unit ball of a given norm of \(X\) in relation to its composition with the polarity map.
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Wijsman and Wijsman regularly triple ideal convergence sequences of sets

Scientific African, 2022
CARLOS Granados, Bright Osu
exaly  

The normality of Wijsman topology of fuzzy metric space

2019
Bashir, Zia, Ullah, Asad
openaire   +1 more source