Physical Sciences and Mathematics Commons^™

Mappings Of Anr's Whose Images Are Anr's, Jung-In Kang Choi

Doctoral Dissertations

Recently, R.J. Daverman and J.J. Walsh modified an example due to J. Taylor to obtain an example of a cell-like map from a compactum with non-trivial shape onto the Hilbert cube Q such that the non-degeneracy set is contained in the countable union of finite dimensional closed subsets of Q. Previously, G. Kozlowski proved that a cell-like map f: X' → X from a compact ANR X' onto a metric space X is a hereditary shape equivalence if there exists a sequence {B_n}∞_n=1 of finite dimensional closed subsets of X such that the non-degeneracy set is contained …