jeckt
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Homework Statement
Identify the compact subsets of \mathbb{R} with topology \tau:= \{ \emptyset , \mathbb{R}\} \cup \{ (-\infty , \alpha) | \alpha \in \mathbb{R}\}.
just need help on how would you actually go about finding it. I usually just find it by thinking about it.
The Attempt at a Solution
- \emptyset
- [a,b] with a,b\in \mathbb{R}
- \{x\} with x\in \mathbb{R}
I was also thinking about subset with only two points e.g. \{ x,y\} with x,y\in \mathbb{R}. They are compact but then...if i can keep doing that i'll get a countable infinite set, hmmm which i think should also be compact.
thanks!
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