Open and closed maps: What good for? I'm wondering what open mappings are actually good for (except for inverse becomes continuous)???
My irritation came since, people stress that an open mapping not necessarily preserves closed sets (well, sure, I mean closed maps are some totally different subject since they don't describe neigbborhoods).
I cannot imagine any other purpose despite quotient maps or homeomorphisms but thats again about some continuity issues; maybe you know some problem where this becomes really important...

A result in complex analysis says that all (non-constant) holomorphic functions are open maps. This allows for all sorts of nifty results, such as this one: an injective holomorphic function can never have zero derivative.
