Kuratowski convergence on compacta and Hausdorff metric convergence on compacta
Brandi, Primo ; Ceppitelli, Rita ; Holá, Ľubica
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 309-318 / Harvested from Czech Digital Mathematics Library
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This paper completes and improves results of [10]. Let $(X,d_{_X})$, $(Y,d_{_Y})$ be two metric spaces and $G$ be the space of all $Y$-valued continuous functions whose domain is a closed subset of $X$. If $X$ is a locally compact metric space, then the Kuratowski convergence $\tau_{_K}$ and the Kuratowski convergence on compacta $\tau_{_K}^c$ coincide on $G$. Thus if $X$ and $Y$ are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology $\tau_{_{AW}}$ (generated by the box metric of $d_{_X}$ and $d_{_Y}$) and $\tau_{_K}^c$ convergence on $G$, which improves the main result of [10]. In the second part of paper we extend the definition of Hausdorff metric convergence on compacta for general metric spaces $X$ and $Y$ and we show that if $X$ is locally compact metric space, then also $\tau$-convergence and Hausdorff metric convergence on compacta coincide in $G$.

Publié le : 1999-01-01
Classification:  54A20,  54B20,  54C35 
@article{119086,
     author = {Primo Brandi and Rita Ceppitelli and \v Lubica Hol\'a},
     title = {Kuratowski convergence on compacta and Hausdorff metric convergence on compacta},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {309-318},
     zbl = {0976.54010},
     mrnumber = {1732651},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119086}
}

Brandi, Primo; Ceppitelli, Rita; Holá, Ľubica. Kuratowski convergence on compacta and Hausdorff metric convergence on compacta. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 309-318. http://gdmltest.u-ga.fr/item/119086/

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