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If the pointwise convergence of
Wijsman convergence is replaced by uniform convergence (uniformly in
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Z. Frolík, Concerning topological convergence of sets, Czechoskovak Math. J. 10 (1960), 168–180
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522:{\displaystyle d_{\mathrm {H} }(A,B)=\sup _{x\in X}{\big |}d(x,A)-d(x,B){\big |}.}
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606:"Convergence of sequences of convex sets, cones and functions. II"
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27:. Intuitively, Wijsman convergence is to convergence in the
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The
Wijsman topology depends very strongly on the metric
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Beer, Gerald (1994). "Wijsman convergence: a survey".
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184:{\displaystyle d(x,A)=\inf _{a\in A}d(x,a).}
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535:The Hausdorff and Wijsman topologies on Cl(
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55:. Yet earlier, Hausdorff in his book
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354:) with the Wijsman topology is a
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730:Encyclopedia of Mathematics
604:Wijsman, Robert A. (1966).
539:) coincide if and only if (
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369:. Moreover, one has the
723:Som Naimpally (2001) ,
23:suitable for work with
610:Trans. Amer. Math. Soc
570:Kuratowski convergence
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350:metric space, then Cl(
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725:"Wijsman convergence"
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371:Levi-Lechicki theorem
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33:pointwise convergence
21:Hausdorff convergence
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37:uniform convergence
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319:Properties
198:) of sets
105:and a set
73:Definition
735:EMS Press
489:−
456:∈
348:separable
267:→
153:∈
745:Category
559:See also
344:complete
305:topology
711:1285822
684:1269778
640:0196599
632:1994611
547:) is a
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43:History
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334:: if (
307:on Cl(
65:; for
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628:JSTOR
591:Notes
77:Let (
670:ISBN
699:doi
618:doi
614:123
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385:Cl(
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361:Cl(
215:to
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