Michael's Questions of Strict Contractibility
by
Jerzy Dydak
University of Tennessee
Coauthors: J.Segal, S.Spiez

A space X is strictly contractible to a point x₀ in X if there exists a homotopy H:X×[0, 1] --> X starting at identity such that H(x, t)=x₀ if and only if either x=x₀ or t=1. E. Michael proved [11] that if E is locally compact and non-compact space then E×0 is a perfect retract of the product E×[0, 1) if and only if the one-point compactification E^*=E \cup x^* of E is strictly contractible to x^*. We answer some questions posed by E. Michael in [11] and we characterize strictly contractible ANRs in shape-theoretic terms.

Date received: June 22, 2000