Attouch-Wets convergence and Kuratowski convergence on compact sets
Piccione, Paolo ; Sampalmieri, Rosella
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 551-562 / Harvested from Czech Digital Mathematics Library
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Let $X$ be a locally connected, $b$-compact metric space and $E$ a closed subset of $X$. Let $\Bbb G$ be the space of all continuous real-valued functions defined on some closed subsets of $E$. We prove the equivalence of the ${\tau_{_{a\!w}}}$ and ${\tau^c_{_{\!K}}}$ topologies on $\Bbb G$, where $\tau_{_{a\!w}}$ is the so called {\sl Attouch-Wets\/} topology, defined in terms of uniform convergence of distance functionals, and ${\tau^c_{_{\!K}}}$ is the topology of Kuratowski convergence on compacta.

Publié le : 1995-01-01
Classification:  49J52,  54C35,  54C99 
@article{118784,
     author = {Paolo Piccione and Rosella Sampalmieri},
     title = {Attouch-Wets convergence and Kuratowski convergence on compact sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {551-562},
     zbl = {0844.54010},
     mrnumber = {1364496},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118784}
}

Piccione, Paolo; Sampalmieri, Rosella. Attouch-Wets convergence and Kuratowski convergence on compact sets. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 551-562. http://gdmltest.u-ga.fr/item/118784/

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