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From Path Lifting and Unique Arc Lifting to Unique Path Lifting

Published online by Cambridge University Press:  20 November 2018

Harold Bell  and
Gerald S. Ungar
Harold Bell
Affiliation:
University of Cincinnati, Cincinnati, Ohio
Gerald S. Ungar
Affiliation:
University of Cincinnati, Cincinnati, Ohio
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In [4] it was conjectured that a light map p : E → B for which paths can be lifted and lifting of arcs is unique is a Serre fibration. As is well-known this implies that paths have unique liftings. In this paper we shall prove several special cases of this conjecture.

The two main theorems are: (3.5) Let p be a light compact map of a metric space E onto a connected semi-locally contractible along arcs metric space B. If arcs can be lifted uniquely then p is locally trivial.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 204 - 212
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bing, R. H., A convex metric with unique segments, Proc. Amer. Math. Soc. 4 (1953), 167–174.Google Scholar
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3. Rolfsen, D., Geometric methods in topological spaces, Topology Conference, Arizona State University, 1967 (Edited by Grace, E. E.).Google Scholar
4. Ungar, G. S., Light fiber maps, Fund. Math. 62 (1968), 31–45.Google Scholar