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A pullback theorem for locally-equiconnected spaces. (English) Zbl 0595.55007

A space X is locally equiconnected (L.E.C.) if the inclusion of the diagonal \(\Delta\) X in \(X\times X\) is a cofibration. This paper contains the following result. Given any fibration \(p: E\to B\) and map \(f: X\to B\) where E, B and X are all LEC, then the pullback space \(X\varsubsetneq E=\{(x,e):\quad f(x)=p(e)\}\) is also LEC. This can be applied to construct for fibrations with path connected fibres, translation functions between fibres that are base point preserving [c.f. the author, Pac. J. Math. 117, 267-289 (1985; Zbl 0571.55002)].
Reviewer: T.Porter

MSC:

55P05 Homotopy extension properties, cofibrations in algebraic topology
54F99 Special properties of topological spaces
55R05 Fiber spaces in algebraic topology

Citations:

Zbl 0571.55002
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References:

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