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## Main Question or Discussion Point

Self studying here :D....

Let X and Y be noncompact, locally compact hausdorff spaces and let f: X--->Y be a map between them; show that this map extends to a continuous map f* : X* ---> Y* iff f is proper, where X* and Y* are the one point compactifications of X and Y.

(A continuous map is said to be proper if the inverse image of each compact subset of Y is compact in X).

I have already shown that X* is a compact hausdorff space and that X is open and dense in X* and has the subspace topology.

This one might take me awhile to work all the way through, i've meditated on the matter a bit but would appreciate some help getting my foot in the door.

Let X and Y be noncompact, locally compact hausdorff spaces and let f: X--->Y be a map between them; show that this map extends to a continuous map f* : X* ---> Y* iff f is proper, where X* and Y* are the one point compactifications of X and Y.

(A continuous map is said to be proper if the inverse image of each compact subset of Y is compact in X).

I have already shown that X* is a compact hausdorff space and that X is open and dense in X* and has the subspace topology.

This one might take me awhile to work all the way through, i've meditated on the matter a bit but would appreciate some help getting my foot in the door.