Re: difference compact sets

On 30.12.2005 13:03, G.C. wrote:
> Let A and B be two compact sets in R^n.
> Then I think that
> A - B={a-b : a in A, b in B}
> is also compact in R^n.
>
> As a subset of R^n, Heine-Borel suggest it suffices to prove that
> A-B is both closed and bounded.
>
> Or, by definition, given any collection of open sets covering A-B, it's
> possible to costruct a finite sub-covering.
>
> Can you help me in proving that A - B is compact, please?
> Thanks,
> G.C.
>

You could use the fact that the image of a compact set under a
continuous mapping is compact again (in Hausdorff spaces).

J.
.

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