Re: Compact open topology

On 27 Jan., 20:46, Philippe Gaucher <p...@xxxxxxxxxxxxx> wrote:
As set map, hom(X x Y, Z) ---> hom(Y, hom(X,Z)) is always bijective of
course. But take a continuous map f:XxY-->Z, the map f(-,y) is not
necessarily continuous.

Yes, that's what I wanted to say: The TOP map hom(X x Y, Z) --->
hom(Y, hom(X,Z)) does not EXIST in general in TOP, because it is not
continuous, right? But it is always bijective. So the local
compactness of X guarantees the existence in TOP, not the bijectivity.
.

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