From: rusin@washington.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: a question about closed sets
Date: 4 Feb 1995 11:22:53 GMT
In article <3gtolg$lgg@taco.cc.ncsu.edu>,
James Grady Ward wrote:
>
>a question a few of us come up with is
>if you define A+B as {x+y|x in A and y in B}
>we know that if A,B are open the A+B is open,
>
>but if A,B are closed does A+B have to be closed
>
>we made a proof using seqences that the teacher
>said wouldnt work
Your teacher should've given you a counterexample and made _you_ find out
where your proof failed. In R^2, take A={(x,y) | xy=1} and
B={(x,y) | xy=-1}. Find a point not in A+B which lies in the closure
of A+B, and then figure out why your proof doesn't force it to be in A+B
dave