Krasinkiewicz Spaces and Parametric Krasinkiewicz Maps
نویسنده
چکیده
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 g such that all restrictions g|f(y), y ∈ Y , are Krasinkiewicz maps. The same conclusion remains true if M is homeomorphic to a closed convex subset of a Banach space and X is a C-space.
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