List questions from baire-category

Published on 15 May 2015 - 22:42

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Show that $\mathbb{R}^n$ cannot be written as a countable union of proper subspaces

Published on 16 May 2015 - 1:44

1.3k

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Show that a countable dense subset $D \subset X$ is not a $G_{\delta}$

Published on 16 May 2015 - 20:06

318

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Q: Nowhere dense sets.

Published on 17 May 2015 - 3:13

1.4k

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Hölder continuous functions are of 1st category in $C[0,1]$

Published on 29 Mar 2026 - 4:17

2.4k

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Prob. 5, Sec. 27 in Munkres' TOPOLOGY, 2nd ed: Every compact Hausdorff space is a Baire space

Published on 24 May 2015 - 13:07

1.6k

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Baire Category theorem - Determining First or Second Category

Published on 30 May 2015 - 0:31

152

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Closed subsets of empty interior are of 1st category

Published on 30 May 2015 - 16:55

258

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Is the closure of a meager set meager?

Published on 30 May 2015 - 22:47

220

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Undestanding an assumption in Baire's theorem proof.

Published on 09 Jun 2015 - 22:33

412

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The set of continuity of a pointwise limit of continuous functions

Published on 05 Jul 2015 - 11:07

205

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Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.

Published on 24 Jul 2015 - 11:24

2.6k

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Dense $G_{\delta}$ set implies comeagre set

Published on 25 Jul 2015 - 14:13

274

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Is $C[0,1]$ equipped with $\lVert \cdot \rVert_1$ a countable union of nowhere dense sets?

Published on 28 Jul 2015 - 18:21

224

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Application of Baire Category theorem

Published on 27 Mar 2026 - 0:02

List Question

Requirements for the principle of uniform boundedness

Show that $\mathbb{R}^n$ cannot be written as a countable union of proper subspaces

Show that a countable dense subset $D \subset X$ is not a $G_{\delta}$

Q: Nowhere dense sets.

Hölder continuous functions are of 1st category in $C[0,1]$

Prob. 5, Sec. 27 in Munkres' TOPOLOGY, 2nd ed: Every compact Hausdorff space is a Baire space

Baire Category theorem - Determining First or Second Category

Closed subsets of empty interior are of 1st category

Is the closure of a meager set meager?

Undestanding an assumption in Baire's theorem proof.

The set of continuity of a pointwise limit of continuous functions

Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.

Dense $G_{\delta}$ set implies comeagre set

Is $C[0,1]$ equipped with $\lVert \cdot \rVert_1$ a countable union of nowhere dense sets?

Application of Baire Category theorem

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