Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658448 | Topology and its Applications | 2014 | 12 Pages |
Abstract
We study the behaviour of fibre maps under exponentiation, i.e. given a fibration p:EâB we ask for which spaces X is the induced map between mapping spaces pâ:EXâBX also a fibration. If X is a locally compact space, the positive answer follows easily by the exponential law so in this paper we consider more general spaces and show that the preservation of fibrations is related to the local homotopy properties of the space X. For example, if p is a Dold fibration and X admits a deformation retraction on a compactly generated space, then the induced map pâ is also a Dold fibration. Similar results hold for Hurewicz fibrations with unique path-lifting and for covering spaces, and can be furthermore extended to spaces that admit some numerable cover, whose elements preserve fibration property.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Petar PaveÅ¡iÄ,