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Rendiconti del Circolo Matematico di Palermo : Volume 66

Rendiconti del Circolo Matematico di Palermo : Volume 65

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Rendiconti del Circolo Matematico di Palermo : Volume 58

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Rendiconti del Circolo Matematico di Palermo : Volume 47

Rendiconti del Circolo Matematico di Palermo : Volume 46

Rendiconti del Circolo Matematico di Palermo : Volume 46, Issue 3, September 1997

Rendiconti del Circolo Matematico di Palermo : Volume 46, Issue 2, June 1997

Rendiconti del Circolo Matematico di Palermo : Volume 46, Issue 1, February 1997

Non-existence of one-signed solutions for variational equations with locally amplifying potentials

On the hypergroups with four proper pairs and two or three non-scalar elements

Wijsman topology on function spaces

Cyclic actions on compression bodies

Fixed points of asymptotically regular semigroups in Banach spaces

On the representation of partially ordered sets

An upper bound for the zeros of the derivative of Bessel functions

Operateurs essentiellement reguliers dans les espaces de Banach

Wijsman topology on function spaces

Content Provider	Springer Nature Link
Author	Maio, Giuseppe Holà, Ľubica
Copyright Year	1997
Abstract	LetC(X,Y) be the space of continuous functions from a metric space (X,d) to a metric space (Y, e).C(X, Y) can be thought as subset of the hyperspaceCL(X×Y) of closed and nonempty subsets ofX×Y by identifying each element ofC(X,Y) with its graph. We considerC(X,Y) with the topology inherited from the Wijsman topology induced onCL(X×Y) by the box metric ofd ande. We study the relationships between the Wijsman topology and the compact-open topology onC(X,Y) and also conditions under which the Wijsman topology coincide with the Fell topology. Sufficient conditions under which the compactopen topology onC(X,Y) is weaker than the Wijsman topology are given (IfY is totally bounded, then for every metric spaceX the compactopen topology onC(X,Y) is weaker than the Wijsman topology and the same is true forX locally connected andY rim-totally bounded). We prove that a metric spaceX is boundedly compact iff the Wijsman topology onC(X, ℝ) is weaker than the compact-open topology. We show that ifX is a σ-compact complete metric space andY a compact metric space, then the Wijsman topology onC(X,Y) is Polish.
Starting Page	52
Ending Page	70
Page Count	19
File Format	PDF
ISSN	0009725X
Journal	Rendiconti del Circolo Matematico di Palermo
Volume Number	46
Issue Number	1
e-ISSN	19734409
Language	English
Publisher	Springer-Verlag
Publisher Date	1997-01-01
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Wijsman topology hyperspace metric space totally bounded rim-compact rim-totally bounded pointwise convergence compact-open topology Fell topology Subspaces Metric spaces, metrizability Hyperspaces Mathematics Algebra Geometry Analysis Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Fell topology on the hyperspace of a non-Hausdorff space

Uniform Continuity, Uniform Convergence, and Shields

Fell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence

Gap, Excess and Bornological Convergence

The hyperspace of the regions below continuous maps with the fell topology

Fell topology on the space of functions with closed graph

Weightable quasi-uniformities

Completeness of hyperspaces of compact subsets of quasi-metric spaces

Note on hit-and-miss topologies

Wijsman topology on function spaces

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Wijsman topology on function spaces