The Stacks project

Change definition proper map topological spaces

Thanks to Brian Conrad

The comments in the introduction to the section discussing proper maps
of topological spaces are thanks to Brian.

Proper base change sheaves sets topology

Fix compile problem

Upgrade proper base change theorem in topology

Thanks to Brian Conrad who writes

"Johan, I noticed that the Stacks Project has a proper base change theorem
in topology, but it is plagued by unnecessary hypotheses.  In
SGA4, Exp. V_{bis}, 4.1, 4.2 Deligne gives a very slick proof of that
base-change isomorphism for proper maps between arbitrary topological
spaces, where proper := separated + universal closed =
separated + closed + compact fibers.  This generality deserves to be
more widely known."

The proof in the Stacks project is not as slick because we don't use the
notion of "mou" sheaves. (Wikipedia says "mou" = "soft".) Our approach
uses Cech cohomology and therefore needs some lemmas on the existence of
suitable open coverings...

Tags: Added new tags

Proper base change (topological case)