Answer by Matematleta for If $X$ is compact, then every sequence in $X$ has a...
We can use the fact that a metrizable space is sequentially compact iff it is compact. Then, take $\beta \mathbb Z$, and suppose it is metrizable. Then, since $\mathbb Z$ is not compact, there is an...
View ArticleAnswer by halrankard2 for If $X$ is compact, then every sequence in $X$ has a...
There appears to be some wires crossed in your textbook. The cofinite topology always has the property that every sequence contains a convergent subsequence. This is simply because every open set...
View ArticleIf $X$ is compact, then every sequence in $X$ has a convergent subsequence.
The following is the text given from a textbook:"Statement: If $X$ is compact, then every sequence in $X$ has a convergent subsequence.This statment is false. The counter example is given by the...
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