Question

Partitions of unity $\Leftrightarrow$ Hausdorff + Second-countable (in locally Euclidean space)

score 699 · Answer 1 · 2026-05-13 13:54:57

699

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Partitions of unity $\Leftrightarrow$ Hausdorff + Second-countable (in locally Euclidean space)

Published on 13 May 2026 - 13:54

score 51 · Answer 2 · 2026-04-12 15:21:12

51

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Lemma 1 of Meyer 1969 ''Sequential properties of ordered topological spaces''

Published on 12 Apr 2026 - 15:21

score 60 · Answer 3 · 2026-04-29 12:33:39

60

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The use of the Axiom of Choice in this proof of the sequence lemma

Published on 29 Apr 2026 - 12:33

score 717 · Answer 4 · 2026-04-12 00:09:46

717

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Compact set always contains its sup and inf

Published on 12 Apr 2026 - 0:09

score 448 · Answer 5 · 2026-04-09 09:51:49

448

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A connected, but not path-connected, space whose fundamental group depends on the basepoint

Published on 09 Apr 2026 - 9:51

score 295 · Answer 6 · 2026-04-15 22:19:19

295

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Poincare duality in Bott Tu Differential Forms in Algebraic Topology

Published on 15 Apr 2026 - 22:19

score 55 · Answer 7 · 2026-04-16 21:05:33

55

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Proving $f(x,y)=\left ( \frac{1}{4}\sin(x+y),1+\frac{2}{3}\arctan(x-y) \right )$ is a contraction

Published on 16 Apr 2026 - 21:05

score 612 · Answer 8 · 2026-04-13 02:06:40

612

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A subset of a metric space is open iff it is a union of open neighborhoods.

Published on 13 Apr 2026 - 2:06

score 1.1k · Answer 9 · 2026-04-16 10:57:42

1.1k

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Is $ C ^ 1 [ 0 , 1 ] $ compact? Is the closure of the unit ball of $ C ^ 1 [ 0 , 1 ] $ in $ C [ 0 , 1 ] $ compact?

Published on 16 Apr 2026 - 10:57

score 355 · Answer 10 · 2026-04-12 03:20:47

355

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Is a simply connected subset of $\mathbb{R}^n$ necessarily measurable?

Published on 12 Apr 2026 - 3:20

score 59 · Answer 11 · 2026-05-11 00:42:02

59

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Smooth endpoint map

Published on 11 May 2026 - 0:42

score 237 · Answer 12 · 2026-04-11 21:27:10

237

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Properties of upper triangular matrix

Published on 11 Apr 2026 - 21:27

score 192 · Answer 13 · 2026-04-10 16:45:03

192

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How can i prove that? Connected components and continuous function

Published on 10 Apr 2026 - 16:45

score 119 · Answer 14 · 2026-04-09 14:59:56

119

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About problem of baby Rudin basic topology

Published on 09 Apr 2026 - 14:59

score 215 · Answer 15 · 2026-04-12 09:29:47

215

Views

Connected component

Published on 12 Apr 2026 - 9:29

List Question

Partitions of unity $\Leftrightarrow$ Hausdorff + Second-countable (in locally Euclidean space)

Lemma 1 of Meyer 1969 ''Sequential properties of ordered topological spaces''

The use of the Axiom of Choice in this proof of the sequence lemma

Compact set always contains its sup and inf

A connected, but not path-connected, space whose fundamental group depends on the basepoint

Poincare duality in Bott Tu Differential Forms in Algebraic Topology

Proving $f(x,y)=\left ( \frac{1}{4}\sin(x+y),1+\frac{2}{3}\arctan(x-y) \right )$ is a contraction

A subset of a metric space is open iff it is a union of open neighborhoods.

Is $ C ^ 1 [ 0 , 1 ] $ compact? Is the closure of the unit ball of $ C ^ 1 [ 0 , 1 ] $ in $ C [ 0 , 1 ] $ compact?

Is a simply connected subset of $\mathbb{R}^n$ necessarily measurable?

Smooth endpoint map

Properties of upper triangular matrix

How can i prove that? Connected components and continuous function

About problem of baby Rudin basic topology

Connected component

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