Question

How does partition of unity imply that for a compact $D$, there is only finitely many $ \operatorname{Support}\phi_i$ that intersect with $D$?

score 250 · Answer 1 · 2026-03-26 06:15:12

250

Views

How does partition of unity imply that for a compact $D$, there is only finitely many $ \operatorname{Support}\phi_i$ that intersect with $D$?

Published on 26 Mar 2026 - 6:15

score 31 · Answer 2 · 2018-07-02 16:04:13

31

Views

Verifying my proof of relative compactness (Rudin's definitions)

Published on 02 Jul 2018 - 16:04

score 112 · Answer 3 · 2026-03-25 03:17:09

112

Views

Cut Point along every geodesic implies Compactness

Published on 25 Mar 2026 - 3:17

score 223 · Answer 4 · 2026-03-25 18:03:18

223

Views

The étale topos is coherent: does the scheme need to be quasicompact?

Published on 25 Mar 2026 - 18:03

score 411 · Answer 5 · 2018-07-03 09:59:45

411

Views

Compactness of unitary group

Published on 03 Jul 2018 - 9:59

score 902 · Answer 6 · 2018-07-03 23:18:21

902

Views

Metrizability of Hausdorff continuous image of compact metric space

Published on 03 Jul 2018 - 23:18

score 70 · Answer 7 · 2018-07-04 11:51:57

70

Views

If $K\subset Y$, does it necessarily mean that an open cover of $K$ exists in $Y$?

Published on 04 Jul 2018 - 11:51

score 85 · Answer 8 · 2018-07-05 06:29:07

85

Views

Compact subset of $\Bbb{R}^2$

Published on 05 Jul 2018 - 6:29

score 69 · Answer 9 · 2018-07-05 15:33:02

69

Views

Let $f:X\rightarrow Y$ be continuous and $X$ be compact. Then $f(X)\subseteq Y$ is compact.

Published on 05 Jul 2018 - 15:33

score 47 · Answer 10 · 2018-07-06 00:14:29

47

Views

If $\overline{U \cap Z}$ is compact in $\bar U$, how does it follow that $\overline{U \cap Z}$ is compact in $Z$?

Published on 06 Jul 2018 - 0:14

score 117 · Answer 11 · 2026-03-25 09:37:09

117

Views

Uniform bound on a compact space (by Taylor expansion?)

Published on 25 Mar 2026 - 9:37

score 244 · Answer 12 · 2018-07-10 08:44:29

244

Views

Generalized Method for Constrained Extrema on non-compact set

Published on 10 Jul 2018 - 8:44

score 90 · Answer 13 · 2026-03-25 13:56:46

90

Views

Prove and disprove compactness of balls w.r.t. a given metric

Published on 25 Mar 2026 - 13:56

score 76 · Answer 14 · 2018-07-11 07:11:26

76

Views

Sum of locally compact spaces is locally compact

Published on 11 Jul 2018 - 7:11

score 344 · Answer 15 · 2018-07-11 14:09:13

344

Views

Other examples of a "standard compactness argument"?

Published on 11 Jul 2018 - 14:09

List Question

How does partition of unity imply that for a compact $D$, there is only finitely many $ \operatorname{Support}\phi_i$ that intersect with $D$?

Verifying my proof of relative compactness (Rudin's definitions)

Cut Point along every geodesic implies Compactness

The étale topos is coherent: does the scheme need to be quasicompact?

Compactness of unitary group

Metrizability of Hausdorff continuous image of compact metric space

If $K\subset Y$, does it necessarily mean that an open cover of $K$ exists in $Y$?

Compact subset of $\Bbb{R}^2$

Let $f:X\rightarrow Y$ be continuous and $X$ be compact. Then $f(X)\subseteq Y$ is compact.

If $\overline{U \cap Z}$ is compact in $\bar U$, how does it follow that $\overline{U \cap Z}$ is compact in $Z$?

Uniform bound on a compact space (by Taylor expansion?)

Generalized Method for Constrained Extrema on non-compact set

Prove and disprove compactness of balls w.r.t. a given metric

Sum of locally compact spaces is locally compact

Other examples of a "standard compactness argument"?

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