Re: Local Homeomorphisms

On 20.04.2008 10:48, William Elliot wrote:
On Fri, 18 Apr 2008, Jannick Asmus wrote:
On 18.04.2008 12:13, William Elliot wrote:

What's the trace topology?

.... the induced topology on a subset, cf., e.g., http://en.wikipedia.org/wiki/Subspace_topology.

Google might become your friend one day. ;)

Let f:X -> Y be a continuous bijection, X locally compact, Y Hausdorff.
Is f a local homeomorphism? Well clearly for all x, some
open U nhood x with U homeomorphic f(U), but is f(U) open?
Certainly not: identity map (R,discrete topology) -> (R,norm topology).

Another counter example is f:[0,1) -> S^1.

Right.

It appears than in the notion of covering map, that the local
homeomorphism has f(U) being open, not by the definition of
local homeomorphism, but by the definition of covering map.

In other words
covering map --> local homeomorphism with open local images.

This is just convention - as I said already.

Some compact K with x in int K
f:int K -> Y closed continuous bijection.
int K homeomorphic f(int K)

Why is f(int K) open, or is it?

HTH.

HTH ?
Convention - like "nhood". I do not want to argue about something like
this. ;)

What's the definition of HTH?

Google should become your friend.

HTH.

Best wishes,
J.
.

Relevant Pages

  • Re: Local Homeomorphisms
    ... Now Yahoo is my friend. ... local homeomorphism, but by the definition of covering map. ... covering map --> local homeomorphism with open local images. ... Google should become your friend. ...
    (sci.math)
  • Re: Local Homeomorphisms
    ... On 20.04.2008 11:37, William Elliot wrote: ... covering map --> local homeomorphism with open local images. ... since homeomorphism basically means that f induces a bijection of the open sets of two topological spaces. ...
    (sci.math)