Silly Mistake August 15, 2009
Posted by putnam120 in Math Related.trackback
I was on a math help forum and was trying to help someone with the following problem.
Given two disjoint closed sets and
in a metric space
, prove that there exists disjoint open sets
and
such that
and
.
In my proof I made the following mistake: Let for
,
. Then
.
I should have stopped at this time, since I remember talking about something very similar to this in my analysis class. It turns out that to gaurantee you need that at least one of
to be compact.
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