New posts in baire-category

There exist meager subsets of $\mathbb{R}$ whose complements have Lebesgue measure zero

real-analysis general-topology measure-theory baire-category

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

real-analysis general-topology functional-analysis baire-category holder-spaces

For a differentiable function $f$ show that $\{x:\limsup_{y\to x}|f'(y)|<\infty\} $ is open and dense in $\mathbb R$

real-analysis general-topology baire-category

The Principle of Condensation of Singularities

functional-analysis banach-spaces operator-theory normed-spaces baire-category

Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set

real-analysis baire-category

With the condition $\lim_{x\to\infty}(f(x+a)−f(x))=0$, how to prove that $f(x)$ is uniformly continuous?

real-analysis calculus general-topology baire-category

Equivalence of Baire Space definitions

general-topology baire-category

intuition of decomposition of $\mathbb{R}$ into disjoint union of first category and null set

real-analysis measure-theory real-numbers baire-category

An application of Baire Category Theorem

real-analysis functional-analysis bounded-variation baire-category

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

general-topology compactness solution-verification baire-category

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

real-analysis metric-spaces baire-category

Diophantine number has full measure but is meager

real-analysis functional-analysis baire-category

Definitions of Baire first and second category sets

general-topology baire-category

Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?

real-analysis inequality metric-spaces baire-category

Complete space as a disjoint countable union of closed sets

general-topology metric-spaces examples-counterexamples connectedness baire-category

Can a sequence of functions have infinity as limit exactly at rationals?

real-analysis sequences-and-series baire-category

Examples of closed sets with empty interior

real-analysis general-topology examples-counterexamples baire-category

What is the intuition behind the terminology surrounding Baire's Theorem?

general-topology functional-analysis baire-category

Prove $\ell_1$ is first category in $\ell_2$

analysis functional-analysis baire-category

(ZF) If $\mathbb{R}^k$ is a countable union of closed sets, then at least one has a nonempty interior

general-topology set-theory axiom-of-choice baire-category