Question

If for some sequence $a_n\to \infty$ the limit $\lim_{n\to\infty} f(a_nx)$ exists for all $x\in\mathbb R$, then $\lim_{x\to\infty} f(x)$ exists

score 115 · Answer 1 · 2026-04-16 02:29:24

115

Views

If for some sequence $a_n\to \infty$ the limit $\lim_{n\to\infty} f(a_nx)$ exists for all $x\in\mathbb R$, then $\lim_{x\to\infty} f(x)$ exists

Published on 16 Apr 2026 - 2:29

score 51 · Answer 2 · 2026-04-15 00:17:18

51

Views

A multivariable complex analysis problem probably related with Baire Category Theorem

Published on 15 Apr 2026 - 0:17

score 253 · Answer 3 · 2026-04-16 11:13:23

253

Views

Proving that $\left[ 0,1 \right] $ is not the countable union of disjoint closed intervals using Baire Category Theorem

Published on 16 Apr 2026 - 11:13

score 268 · Answer 4 · 2026-04-12 07:49:03

268

Views

Proof of Lemma preceding Principle of Condensation of Singularities

Published on 12 Apr 2026 - 7:49

score 1.3k · Answer 5 · 2026-04-14 17:31:23

1.3k

Views

Isolated points in a complete metric space

Published on 14 Apr 2026 - 17:31

score 164 · Answer 6 · 2026-04-13 15:55:04

164

Views

Baire's Theorem: Examples for open dense subsets

Published on 13 Apr 2026 - 15:55

score 467 · Answer 7 · 2026-04-16 08:33:06

467

Views

The only meagre and open set is the empty set?

Published on 16 Apr 2026 - 8:33

score 315 · Answer 8 · 2026-04-11 04:47:25

315

Views

Meager topological spaces of uncountable size

Published on 11 Apr 2026 - 4:47

score 40 · Answer 9 · 2026-04-16 13:49:11

40

Views

Notation question: $T[X]=\bigcup\limits_{n=1}^{\infty} nT[B]$.

Published on 16 Apr 2026 - 13:49

score 91 · Answer 10 · 2026-04-16 05:50:51

91

Views

Proving that this set of cantor functions is dense and $G_\delta$.

Published on 16 Apr 2026 - 5:50

score 274 · Answer 11 · 2026-04-15 14:52:14

274

Views

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

Published on 15 Apr 2026 - 14:52

score 49 · Answer 12 · 2026-04-16 16:07:12

49

Views

Connected metric space of first category

Published on 16 Apr 2026 - 16:07

score 63 · Answer 13 · 2026-04-16 21:24:50

63

Views

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Published on 16 Apr 2026 - 21:24

score 154 · Answer 14 · 2026-04-16 19:25:52

154

Views

Hints to show that $A_{n}$ is nowhere dense in $C([0,1])$

Published on 16 Apr 2026 - 19:25

score 86 · Answer 15 · 2026-04-14 13:39:35

86

Views

Understanding proof of Poincaré recurrence theorem in Measure and Category (Oxtoby)

Published on 14 Apr 2026 - 13:39

List Question

If for some sequence $a_n\to \infty$ the limit $\lim_{n\to\infty} f(a_nx)$ exists for all $x\in\mathbb R$, then $\lim_{x\to\infty} f(x)$ exists

A multivariable complex analysis problem probably related with Baire Category Theorem

Proving that $\left[ 0,1 \right] $ is not the countable union of disjoint closed intervals using Baire Category Theorem

Proof of Lemma preceding Principle of Condensation of Singularities

Isolated points in a complete metric space

Baire's Theorem: Examples for open dense subsets

The only meagre and open set is the empty set?

Meager topological spaces of uncountable size

Notation question: $T[X]=\bigcup\limits_{n=1}^{\infty} nT[B]$.

Proving that this set of cantor functions is dense and $G_\delta$.

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

Connected metric space of first category

Two versions of Baire Category Theorem for Profinite Groups

Hints to show that $A_{n}$ is nowhere dense in $C([0,1])$

Understanding proof of Poincaré recurrence theorem in Measure and Category (Oxtoby)

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