Question

The pre-image of a set boundary is included in the boundary of the pre-image of the set: the $R^m$ case

score 921 · Answer 1 · 2026-04-13 20:59:16

921

Views

The pre-image of a set boundary is included in the boundary of the pre-image of the set: the $R^m$ case

Published on 13 Apr 2026 - 20:59

score 213 · Answer 2 · 2026-04-14 15:15:06

213

Views

The image of a continuous mapping on a connected metric space is connected: ($\epsilon - \delta$) proof

Published on 14 Apr 2026 - 15:15

score 128 · Answer 3 · 2026-04-17 06:37:48

128

Views

Topology on a product space, such that the projection is not continuous

Published on 17 Apr 2026 - 6:37

score 111 · Answer 4 · 2026-04-11 16:40:16

111

Views

Sufficient conditions for minimum to exist in non-compact subset of normed vector space

Published on 11 Apr 2026 - 16:40

score 60 · Answer 5 · 2026-05-11 02:50:20

60

Views

What separation axiom is necessary for existence of neighborhood which closure is a subset of another given neighborhood

Published on 11 May 2026 - 2:50

score 200 · Answer 6 · 2026-04-14 06:54:14

200

Views

Given a non-countable subset $X$ of $\mathbb{R}$, prove that $X'$ is uncountable

Published on 14 Apr 2026 - 6:54

score 284 · Answer 7 · 2026-04-15 11:32:22

284

Views

Inverse Limit Space (Homeomorphism)

Published on 15 Apr 2026 - 11:32

score 89 · Answer 8 · 2026-05-10 16:47:45

89

Views

Equivalent condition of a diffeomorphism having a dense orbit

Published on 10 May 2026 - 16:47

score 32 · Answer 9 · 2026-04-14 23:19:22

32

Views

Characterization of ω-cover by co-zero sets.

Published on 14 Apr 2026 - 23:19

score 153 · Answer 10 · 2026-04-13 20:03:45

153

Views

The image of totally disconnected compacta under Lipschitz maps

Published on 13 Apr 2026 - 20:03

score 58 · Answer 11 · 2026-04-16 08:56:13

58

Views

Decompose a unit ball into 3 convex disjoint parts parts with common boundary

Published on 16 Apr 2026 - 8:56

score 357 · Answer 12 · 2026-05-11 05:08:05

357

Views

Quotient space $[0,1]/C$ is homeomorphic to $[0,1]/\left\{0,1,\frac12,\frac13,...\right\}$, $C$ denotes Cantor set.

Published on 11 May 2026 - 5:08

score 542 · Answer 13 · 2026-04-13 10:24:32

542

Views

Euler’s Characteristic for nonorientable surfaces?

Published on 13 Apr 2026 - 10:24

score 177 · Answer 14 · 2026-04-09 07:06:10

177

Views

Soft question: why define smooth manifolds intrinsically?

Published on 09 Apr 2026 - 7:06

score 580 · Answer 15 · 2026-04-16 05:45:49

580

Views

closure of the set $S=\{(x,y)|x\in(0,1)\cap\mathbb{Q};y=\sin(\frac1x)\}$

Published on 16 Apr 2026 - 5:45

List Question

The pre-image of a set boundary is included in the boundary of the pre-image of the set: the $R^m$ case

The image of a continuous mapping on a connected metric space is connected: ($\epsilon - \delta$) proof

Topology on a product space, such that the projection is not continuous

Sufficient conditions for minimum to exist in non-compact subset of normed vector space

What separation axiom is necessary for existence of neighborhood which closure is a subset of another given neighborhood

Given a non-countable subset $X$ of $\mathbb{R}$, prove that $X'$ is uncountable

Inverse Limit Space (Homeomorphism)

Equivalent condition of a diffeomorphism having a dense orbit

Characterization of ω-cover by co-zero sets.

The image of totally disconnected compacta under Lipschitz maps

Decompose a unit ball into 3 convex disjoint parts parts with common boundary

Quotient space $[0,1]/C$ is homeomorphic to $[0,1]/\left\{0,1,\frac12,\frac13,...\right\}$, $C$ denotes Cantor set.

Euler’s Characteristic for nonorientable surfaces?

Soft question: why define smooth manifolds intrinsically?

closure of the set $S=\{(x,y)|x\in(0,1)\cap\mathbb{Q};y=\sin(\frac1x)\}$

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