If $A$ and $B$ are compact subsets of $\mathbb{R ^ n}$, is then $ A × B $ compact? I think it is because it's then closed and bounded because A and B are closed and bounded?
2026-03-29 22:33:11.1774823591
If $A$ and $B$ are compact subsets of $\mathbb{R}$, is then $ A × B $ compact?
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Your argument is correct.
More generally, of $X$ and $Y$ are any compact topological spaces, $X\times Y$ is compact too, by Tychonoff's theorem.