List questions from baire-category

Published on 29 Apr 2026 - 12:32

252

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Two variants of proof for Baire's category theorem

Published on 29 Apr 2026 - 12:31

287

Views

Understanding a step in Baire Category Theorem

Published on 29 Apr 2026 - 12:31

866

Views

Countable Dense Set not a $G_{\delta}$ set? Where's the contradiction?

Published on 29 Apr 2026 - 12:31

680

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Show that a closed subset is first category.

Published on 29 Apr 2026 - 12:31

128

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Show that the set of $f\in L^{1}$ so that $f\notin L^{p}$ is residual.

Published on 29 Apr 2026 - 12:31

775

Views

$[0,1]$ is uncountable using Baire's Category Theorem

Published on 29 Apr 2026 - 12:31

441

Views

Negation of countable union of nowhere dense.

Published on 29 Apr 2026 - 12:31

1.7k

Views

Is a nowhere dense set closed?

Published on 29 Apr 2026 - 12:31

854

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Show that there is a continuous real function $h$ on $[0,1]$ such that $\lim \sup |\frac{h(x+t)-h(x)}{t}| = \infty$ for all $x \in [0,1)$

Published on 29 Apr 2026 - 12:31

107

Views

Zorn's Lemma in an Oxtoby's theorem

Published on 14 Apr 2026 - 9:58

173

Views

Are the two formulations of Baire category theorem equivalent for arbitrary metric spaces?

Published on 29 Apr 2026 - 12:31

73

Views

Why a set of second category minus (take away) a set of first category is of second category?

Published on 29 Apr 2026 - 12:31

72

Views

On Borel subsets of a topological space

Published on 29 Apr 2026 - 12:31

2.6k

Views

Proving that the set of continuous nowhere differentiable functions is dense using Baire's Category Theorem

Published on 29 Apr 2026 - 12:31

List Question

Subspace $\ell^2$ is of first category

Two variants of proof for Baire's category theorem

Understanding a step in Baire Category Theorem

Countable Dense Set not a $G_{\delta}$ set? Where's the contradiction?

Show that a closed subset is first category.

Show that the set of $f\in L^{1}$ so that $f\notin L^{p}$ is residual.

$[0,1]$ is uncountable using Baire's Category Theorem

Negation of countable union of nowhere dense.

Is a nowhere dense set closed?

Show that there is a continuous real function $h$ on $[0,1]$ such that $\lim \sup |\frac{h(x+t)-h(x)}{t}| = \infty$ for all $x \in [0,1)$

Zorn's Lemma in an Oxtoby's theorem

Are the two formulations of Baire category theorem equivalent for arbitrary metric spaces?

Why a set of second category minus (take away) a set of first category is of second category?

On Borel subsets of a topological space

Proving that the set of continuous nowhere differentiable functions is dense using Baire's Category Theorem

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