• Krasinkiewicz spaces and parametric Krasinkiewicz maps, Vol 36, No.4

Eiichi, Matsuhashi, Department of Mathematics, Faculty of Engineering, Shimane University ,Matsue, Shimane 690-8504, Japan (matsuhashi@riko.shimane-u.ac.jp). and Vesko Valov, Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada (veskov@nipissingu.ca).
Krasinkiewicz spaces and parametric Krasinkiewicz maps, pp. 1207-1220.
ABSTRACT. We say that a metrizable space M is a Krasinkiewicz space if any map from a metrizable compactum X into M can be approximated by Krasinkiewicz maps (a map g : X → M is Krasinkiewicz provided every continuum in X is either contained in a fiber of g or contains a component of a fiber of g). In this paper we establish the following property of Krasinkiewicz spaces: Let f : X → Y be a perfect map between metrizable spaces and M a Krasinkiewicz complete ANR-space. If Y is a countable union of closed finite-dimensional subsets, then the function space C(X,M) with the source limitation topology contains a dense Gδ-subset of maps such that all restrictions g|f-1(y), y in Y, are Krasinkiewicz maps. The same conclusion remains true if M is homeomorphic to a closed convex subset of a Banach space and Y is a C-space.

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Krasinkiewicz spaces and parametric Krasinkiewicz maps, Vol 36, No.4

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