Henno Brandsma

 74 Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$ 56 A map is continuous if and only if for every set, the image of closure is contained in the closure of image 47 Projection map being a closed map 38 Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$ 30 Show that the countable product of metric spaces is metrizable

### Reputation (126,132)

 +60 $[0,1]$ is commonly called the unit interval - is there a similar term for $[-1,1]$? +10 Nagata-Smirnov vs. Urysohn metrization theorems - an example? +10 Continuous function on a closed set is determined by its values on a countable subset +10 Proving that $(0,1)^3$ not homeomorphic to $[0,3)^3$

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 6k general-topology × 3624 556 proof-verification × 392 1k real-analysis × 614 325 continuity × 164 927 metric-spaces × 540 319 functional-analysis × 173 658 compactness × 340 270 examples-counterexamples × 90 560 elementary-set-theory × 409 266 connectedness × 137

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