numerable fiber bundle

(see also *Chern-Weil theory*, parameterized homotopy theory)

For the theory of fiber bundles to be well-behaved one typically needs to restrict to those that have a *local trivialization* not just over any open cover but over a numerable open cover – these are the numerable bundles. Since this condition is automatic if the base space is paracompact the condition is often not made explicit.

**(numerable fiber bundle)**

A fiber bundle over a topological space is called *numerable* if it admits a local trivialization over a numerable open cover.

Various results for classifying spaces that classify arbitrary fiber bundles over paracompact topological spaces generalizes (only) to a classification of numerable bundles over general topological spaces.

The conclusion that the bundle projection of a topological fiber bundle is a Hurewicz fibration follows generally only for numberable bundles (by this Prop.)

Last revised on March 24, 2021 at 11:26:44. See the history of this page for a list of all contributions to it.