Re: A variant of local homeomorphism

On 27-07-2007 11:11, Jose Capco wrote:

Im not sure if Im making sense.. but lets give this a try..

If f:X--> Y is a continuous map between topological spaces.. then does
it make sense saying that "f is local homeomorphism with respect to
closed sets".. ie.

For any point x in X, there is a closed set C containing x such that f|
C is a homeomorphism.

Or is this equivalent to something else? What if X and Y are compact,
Haussdorf, totally disconnected?

If X is Hausdorff (or even T1) it is equivalent to "f is any map".
After all, for any _x_ in X, {x} is a closed set containing _x_ and
the restriction of _f_ to this set is a homeomorphism.

Best regards,

Jose Carlos Santos
.

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