Question

Proving the existence of a non-monotone continuous function defined on $[0,1]$

score 1.4k · Answer 1 · 2013-10-31 05:49:09

1.4k

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Proving the existence of a non-monotone continuous function defined on $[0,1]$

Published on 31 Oct 2013 - 5:49

score 453 · Answer 2 · 2013-11-04 17:03:03

453

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Can somebody help me to understand this? (Baire Category Theorem)

Published on 04 Nov 2013 - 17:03

score 511 · Answer 3 · 2026-03-28 09:45:27

511

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Can a meager linear subspace be written as a countable increasing union of nowhere dense subspaces?

Published on 28 Mar 2026 - 9:45

score 303 · Answer 4 · 2013-11-11 20:07:49

303

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Baire Category Theorem with $G_{\delta}$

Published on 11 Nov 2013 - 20:07

score 3.8k · Answer 5 · 2013-11-12 19:45:07

3.8k

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Examples of rare, meager and nonmeager sets in $\mathbb{R}$

Published on 12 Nov 2013 - 19:45

score 790 · Answer 6 · 2013-11-15 03:36:54

790

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Prove that there doesn't exist any function $f:\mathbb R\to \mathbb R$ that is continuous only at the rational points.

Published on 15 Nov 2013 - 3:36

score 292 · Answer 7 · 2013-12-01 14:36:23

292

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definition of Baire first category set

Published on 01 Dec 2013 - 14:36

score 246 · Answer 8 · 2013-12-04 02:25:35

246

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Cannot understand some parts of proof for R be a countable union of closed sets

Published on 04 Dec 2013 - 2:25

score 2.6k · Answer 9 · 2013-12-09 15:01:29

2.6k

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No infinite-dimensional $F$-space has a countable Hamel basis

Published on 09 Dec 2013 - 15:01

score 141 · Answer 10 · 2013-12-10 15:51:54

141

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Baire Category Theorem: What should we really prove there?

Published on 10 Dec 2013 - 15:51

score 1.2k · Answer 11 · 2013-12-18 18:20:42

1.2k

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Is a Baire Space necessarily complete?

Published on 18 Dec 2013 - 18:20

score 337 · Answer 12 · 2013-12-21 16:07:24

337

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Baire's theorem proof

Published on 21 Dec 2013 - 16:07

score 386 · Answer 13 · 2013-12-29 15:36:41

386

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Why any uncountable $G_\delta$ set of $\mathbb{R}$, has a subset homeomorphic to $[0,1]$

Published on 29 Dec 2013 - 15:36

score 809 · Answer 14 · 2026-03-28 11:34:53

809

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Who are the measurable sets in $\mathbb{R}$

Published on 28 Mar 2026 - 11:34

score 91 · Answer 15 · 2026-03-28 11:34:12

91

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Oxtoby - Thm 6.2 - There exists a strategy in which (A) wins iff $I_1 \cap B$ of first category

Published on 28 Mar 2026 - 11:34

List Question

Proving the existence of a non-monotone continuous function defined on $[0,1]$

Can somebody help me to understand this? (Baire Category Theorem)

Can a meager linear subspace be written as a countable increasing union of nowhere dense subspaces?

Baire Category Theorem with $G_{\delta}$

Examples of rare, meager and nonmeager sets in $\mathbb{R}$

Prove that there doesn't exist any function $f:\mathbb R\to \mathbb R$ that is continuous only at the rational points.

definition of Baire first category set

Cannot understand some parts of proof for R be a countable union of closed sets

No infinite-dimensional $F$-space has a countable Hamel basis

Baire Category Theorem: What should we really prove there?

Is a Baire Space necessarily complete?

Baire's theorem proof

Why any uncountable $G_\delta$ set of $\mathbb{R}$, has a subset homeomorphic to $[0,1]$

Who are the measurable sets in $\mathbb{R}$

Oxtoby - Thm 6.2 - There exists a strategy in which (A) wins iff $I_1 \cap B$ of first category

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