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2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class of compact...
We prove that the set of all Krasinkiewicz maps from a compact metric space to a polyhedron (or a 1-dimensional locally connected continuum, or an n-dimensional Menger manifold, n ≥ 1) is a dense -subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.
This paper completes and improves results of [10]. Let , be two metric spaces and be the space of all -valued continuous functions whose domain is a closed subset of . If is a locally compact metric space, then the Kuratowski convergence and the Kuratowski convergence on compacta coincide on . Thus if and are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology (generated by the box metric of and ) and convergence on ,...
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