Krasinkiewicz spaces and parametric Krasinkiewicz maps
Eiichi Matsuhashi, Vesko Valov

TL;DR
This paper studies Krasinkiewicz spaces, showing that under certain conditions, the space of maps into these spaces contains a dense set of Krasinkiewicz maps with desirable properties.
Contribution
It establishes that for perfect maps between metrizable spaces, the function space contains a dense G_delta set of Krasinkiewicz maps, extending previous understanding of these spaces.
Findings
Dense G_delta subset of Krasinkiewicz maps in function space
Extension of results to spaces homeomorphic to convex subsets of Banach spaces
Applicable to perfect maps with countable union of finite-dimensional subsets
Abstract
We say that a metrizable space is a Krasinkiewicz space if any map from a metrizable compactum into can be approximated by Krasinkiewicz maps (a map is Krasinkiewicz provided every continuum in is either contained in a fiber of or contains a component of a fiber of ). In this paper we establish the following property of Krasinkiewicz spaces: Let be a perfect map between metrizable spaces and a Krasinkiewicz complete -space. If is a countable union of closed finite-dimensional subsets, then the function space with the source limitation topology contains a dense -subset of maps such that all restrictions , , are Krasinkiewicz maps. The same conclusion remains true if is homeomorphic to a closed convex subset of a Banach space and is a -space.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematics and Applications · Homotopy and Cohomology in Algebraic Topology
