Answer by M W for Is a compact set contained in a (countable) ascending union...
Firstly, this is not generally true even in $\mathbb R$. Take $K_n=[-n,-\frac{1}{n}]\cup \{0\} \cup [\frac{1}{n},n]$, then $K=[-1,1]$ is compact, but will not be contained in any $K_n$.Secondly,...
View ArticleAnswer by Robert Israel for Is a compact set contained in a (countable)...
Counterexample: $X = K = [0,1]$, $K_n = \{0\} \cup [1/n, 1]$.
View ArticleIs a compact set contained in a (countable) ascending union of compact sets...
If $X$ is a (Hausdorff) topological space and $K_0\subset K_1\subset...\subset K_n\subset...\subset X$ are compact subsets such that $X=\bigcup_{n\in\mathbb{N}}K_n$, isit true that for any compact...
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