Hi all, I have the following question.(adsbygoogle = window.adsbygoogle || []).push({});

Are the following spaces homeomorphic in the real number space with absolute value topology?

1) [a,b) and (a,b]

2) (a,b) and (r,s)U(u,v) where r < s < u < v.

For 1), I got that they are not homeomorphic because it fails the topological property that sequences in a set converges to a point in the set. As seen, a sequence could converge to a point a in [a,b), which is in the set, but is not contained in the set (a,b].

-Is this correct?

For 2), I'm not really sure at all. I was wondering if I should try to create a function that maps (a,b) to (r,s)U(u,v) and show the properties for homeomorphisms under topological spaces but I can't find out a function.

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# Homework Help: Absolute value topology?

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