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A Stable Converse to the Vietoris-Smale Theorem with Applications to Shape Theory
Our main result says that if /: X -» Y is a map between finite polyhedra which has /¡-connected homotopy fiber, then there is an n such that / X id: X x /" -* Y is homotopic to a map with ^-connected point-inverses.This result is applied to give an …