## A stable converse to the Vietoris-Smale theorem with applications to shape theory

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- by Steve Ferry PDF
- Trans. Amer. Math. Soc.
**261**(1980), 369-386 Request permission

## Abstract:

Our main result says that if $f: X \to Y$ is a map between finite polyhedra which has*k*-connected homotopy fiber, then there is an

*n*such that $f \times {\text {id:}} X \times {I^n} \to Y$ is homotopic to a map with

*k*-connected point-inverses. This result is applied to give an algebraic characterization of compacta shape equivalent to locally

*n*-connected compacta. We also show that a $U{V^1}$ compactum can be “improved” within its shape class until its homotopy theory and strong shape theory are the same with respect to finite dimensional polyhedra.

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## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**261**(1980), 369-386 - MSC: Primary 55R65; Secondary 54C56, 55P55, 57N20, 57Q05, 57Q10
- DOI: https://doi.org/10.1090/S0002-9947-1980-0580894-1
- MathSciNet review: 580894