Question

how to show boundary of either open or closed set is nowhere dense.

score 577 · Answer 1 · 2014-10-24 08:59:48

577

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how to show boundary of either open or closed set is nowhere dense.

Published on 24 Oct 2014 - 8:59

score 1.6k · Answer 2 · 2014-10-28 11:56:36

1.6k

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Proof that every closed subset of $\mathbb R$ is finite or countable or continuum.

Published on 28 Oct 2014 - 11:56

score 43 · Answer 3 · 2014-11-01 11:33:29

43

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For $f :\mathbb R \to \mathbb R $, there exists an $(a,b)$, such that $f$ is bounded on a sequence with limit $x$, for all $x\in(a,b)$

Published on 01 Nov 2014 - 11:33

score 239 · Answer 4 · 2014-11-23 19:30:50

239

Views

baire category and the union of dyadic balls of rational center

Published on 23 Nov 2014 - 19:30

score 62 · Answer 5 · 2014-11-24 12:27:54

62

Views

Baire category theorem in use on a plane

Published on 24 Nov 2014 - 12:27

score 50 · Answer 6 · 2014-11-25 23:07:53

50

Views

Two proofs with possibly Baire category theorem about completness.

Published on 25 Nov 2014 - 23:07

score 1.8k · Answer 7 · 2014-12-05 06:12:42

1.8k

Views

Baire's property iff first category has dense complement.

Published on 05 Dec 2014 - 6:12

score 271 · Answer 8 · 2014-12-09 02:23:11

271

Views

Strong version of Baire Category Theorem

Published on 09 Dec 2014 - 2:23

score 567 · Answer 9 · 2014-12-21 12:37:58

567

Views

Open mapping lemma - are these versions equivalent?

Published on 21 Dec 2014 - 12:37

score 474 · Answer 10 · 2026-02-23 00:49:33

474

Views

Showing the sum of two sets contains an interval - Baire's Theorem?

Published on 23 Feb 2026 - 0:49

score 776 · Answer 11 · 2014-12-24 14:04:11

776

Views

Convergence of a sequence holomorphic functions

Published on 24 Dec 2014 - 14:04

score 165 · Answer 12 · 2014-12-30 11:09:10

165

Views

For every $x \in [a,b] , \exists n_x\in \mathbb Z^+$ such that $f^{(n_x) }(x)=0$ ; then to prove $f$ is a polynomial in $[a,b]$

Published on 30 Dec 2014 - 11:09

score 69 · Answer 13 · 2019-10-07 18:19:52

69

Views

Baire category theorem in a paper of Pontryagin

Published on 07 Oct 2019 - 18:19

score 294 · Answer 14 · 2019-10-24 10:14:54

294

Views

What is the Baire category argument here? (divergence of many Fourier series at one point)

Published on 24 Oct 2019 - 10:14

score 495 · Answer 15 · 2019-10-26 16:09:04

495

Views

Application of Baire Category theorem in $C[0,1]$

Published on 26 Oct 2019 - 16:09

List Question

how to show boundary of either open or closed set is nowhere dense.

Proof that every closed subset of $\mathbb R$ is finite or countable or continuum.

For $f :\mathbb R \to \mathbb R $, there exists an $(a,b)$, such that $f$ is bounded on a sequence with limit $x$, for all $x\in(a,b)$

baire category and the union of dyadic balls of rational center

Baire category theorem in use on a plane

Two proofs with possibly Baire category theorem about completness.

Baire's property iff first category has dense complement.

Strong version of Baire Category Theorem

Open mapping lemma - are these versions equivalent?

Showing the sum of two sets contains an interval - Baire's Theorem?

Convergence of a sequence holomorphic functions

For every $x \in [a,b] , \exists n_x\in \mathbb Z^+$ such that $f^{(n_x) }(x)=0$ ; then to prove $f$ is a polynomial in $[a,b]$

Baire category theorem in a paper of Pontryagin

What is the Baire category argument here? (divergence of many Fourier series at one point)

Application of Baire Category theorem in $C[0,1]$

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