topological submersion

A topological submersion is a map in Top generalising the sort of map that is called a submersion in Diff.

There are two definitions of a topological submersion p:YX:

  • Each point in Y has a neighbourhood U such that p U:Up(U)×Zp(U) is projection on the first factor. Sometimes Z is required to be a cartesian space n, but this is a bit restrictive.

  • Each point p of Y has a local section σ:VY with xV and p=σ(x).

The second definition includes the first as a special case.

Surjective topological submersions form a singleton Grothendieck pretopology on Top.

Revised on August 24, 2011 10:17:46 by Anonymous Coward (