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nonequilibrium
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Counterexample "intersections of 2 compacts is compact"?
Hello,
I'm looking for a counterexample to "If A and B are compact subsets of a topological space X, then [itex]A \cap B[/itex] is compact." It's not for homework.
I found one online, but it talked about "double-pointed" things which I didn't understand... My knowledge is an introductory course in topology: the first four chapters of Munkres.
I realize I have to look for a non-Hausdorff space, but the only one I know
--if I remember correctly--is the cofinite topology (or the related Zariski topology, but I'm not too familiar with that one).
Hello,
I'm looking for a counterexample to "If A and B are compact subsets of a topological space X, then [itex]A \cap B[/itex] is compact." It's not for homework.
I found one online, but it talked about "double-pointed" things which I didn't understand... My knowledge is an introductory course in topology: the first four chapters of Munkres.
I realize I have to look for a non-Hausdorff space, but the only one I know
--if I remember correctly--is the cofinite topology (or the related Zariski topology, but I'm not too familiar with that one).