Physical Sciences and Mathematics Commons^™

On Maps With Continuous Path Lifting, Jeremy Brazas, Atish Mitra

Mathematics Faculty Publications

We study a natural generalization of covering projections defined in terms of unique lifting properties. A map p : E -+ X has the continuous path-covering property if all paths in X lift uniquely and continuously (rel. basepoint) with respect to the compactopen topology. We show that maps with this property are closely related to fibrations with totally path-disconnected fibers and to the natural quotient topology on the homotopy groups. In particular, the class of maps with the continuous path-covering property lies properly between Hurewicz fibrations and Serre fibrations with totally path-disconnected fibers. We extend the usual classification of covering …