Question

Function in which every inverse image of open "interval" is open interval but not continuous.

score 593 · Answer 1 · 2026-04-12 01:04:20

593

Views

Function in which every inverse image of open "interval" is open interval but not continuous.

Published on 12 Apr 2026 - 1:04

score 254 · Answer 2 · 2026-04-24 16:19:45

254

Views

Nonprincipal ultrafilters over $\mathbb{N}$

Published on 24 Apr 2026 - 16:19

score 308 · Answer 3 · 2026-04-13 00:50:56

308

Views

Homeomorphism between a quotient topology on $\mathbb{R}^2$ and $\mathbb{R}$

Published on 13 Apr 2026 - 0:50

score 1k · Answer 4 · 2026-04-11 20:31:04

1k

Views

Is Dictionary Ordering on $\mathbb{R}^2$ Connected?

Published on 11 Apr 2026 - 20:31

score 306 · Answer 5 · 2026-04-16 06:31:31

306

Views

$\det^{-1}(0)$ is a submanifold of $M_2(\mathbb R) \setminus \{0\}$. Is this also a submanifold of the whole space $M_2(\mathbb R)$?

Published on 16 Apr 2026 - 6:31

score 69 · Answer 6 · 2026-04-15 20:31:21

For each prime $p$ let $S_p=\{n\in \mathbb N: \text{n is a multiple of } p\}$. $\mathscr S=\{1\}\cup \{S_p|\text {p is prime}\}$.

score 39 · Answer 7 · 2026-04-15 03:45:02

$a,b \in X$ and $a<b$, then there is a neighbourhood $U$ of $a$ and neighbourhod of $V$ of $b$ such that $x<y$ whenever $x\in U$ and $y \in V$

score 39 · Answer 8 · 2026-04-12 13:31:16

39

Views

Help finding boundary, accumulation, closure set, and boundary of the closure set.

Published on 12 Apr 2026 - 13:31

score 1.1k · Answer 9 · 2026-04-13 17:23:43

1.1k

Views

Prove that $\mathbb{Z}$ is homeomorphic to $\mathbb{N}$

Published on 13 Apr 2026 - 17:23

score 88 · Answer 10 · 2026-04-15 10:51:00

88

Views

Another representation of $S^n$ as a quotient of disk

Published on 15 Apr 2026 - 10:51

score 464 · Answer 11 · 2026-04-11 15:12:16

464

Views

How to prove a Möbius band is not equivalent to a band

Published on 11 Apr 2026 - 15:12

score 127 · Answer 12 · 2026-04-16 09:11:44

127

Views

Prove the set $K = \{\frac{1}{n} \mid n\in \mathbb{N}\}\cup \{0\}$ is compact.

Published on 16 Apr 2026 - 9:11

score 2.7k · Answer 13 · 2026-04-16 17:24:16

2.7k

Views

Show that $B=\{[a, b)\subset R \mid a<b\}$ is basis of topology on $R$

Published on 16 Apr 2026 - 17:24

score 66 · Answer 14 · 2026-04-17 14:19:27

66

Views

a is a cluster point of a set A iff for any $\delta > 0$, the interval $(a-\delta, a+\delta)$ contains infinitely many points of A

Published on 17 Apr 2026 - 14:19

score 866 · Answer 15 · 2026-04-16 07:39:56

866

Views

Prove that the collection of arithmetic progressions $A=A_{a,b}|a,b\in \boldsymbol{Z},$b$\not\equiv 0$ is Basis for topology on $Z$

Published on 16 Apr 2026 - 7:39

List Question

Function in which every inverse image of open "interval" is open interval but not continuous.

Nonprincipal ultrafilters over $\mathbb{N}$

Homeomorphism between a quotient topology on $\mathbb{R}^2$ and $\mathbb{R}$

Is Dictionary Ordering on $\mathbb{R}^2$ Connected?

$\det^{-1}(0)$ is a submanifold of $M_2(\mathbb R) \setminus \{0\}$. Is this also a submanifold of the whole space $M_2(\mathbb R)$?

For each prime $p$ let $S_p=\{n\in \mathbb N: \text{n is a multiple of } p\}$. $\mathscr S=\{1\}\cup \{S_p|\text {p is prime}\}$.

$a,b \in X$ and $a<b$, then there is a neighbourhood $U$ of $a$ and neighbourhod of $V$ of $b$ such that $x<y$ whenever $x\in U$ and $y \in V$

Help finding boundary, accumulation, closure set, and boundary of the closure set.

Prove that $\mathbb{Z}$ is homeomorphic to $\mathbb{N}$

Another representation of $S^n$ as a quotient of disk

How to prove a Möbius band is not equivalent to a band

Prove the set $K = \{\frac{1}{n} \mid n\in \mathbb{N}\}\cup \{0\}$ is compact.

Show that $B=\{[a, b)\subset R \mid a<b\}$ is basis of topology on $R$

a is a cluster point of a set A iff for any $\delta > 0$, the interval $(a-\delta, a+\delta)$ contains infinitely many points of A

Prove that the collection of arithmetic progressions $A=A_{a,b}|a,b\in \boldsymbol{Z},$b$\not\equiv 0$ is Basis for topology on $Z$

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