Question

Exist a norm such that $S= \{x= (x_{1},x_{2}) \in R^{2}| \|x\| \leq 1, x_{2} >0\}$ which isn't open nor closed?

score 36 · Answer 1 · 2026-04-15 22:16:55

36

Views

Exist a norm such that $S= \{x= (x_{1},x_{2}) \in R^{2}| \|x\| \leq 1, x_{2} >0\}$ which isn't open nor closed?

Published on 15 Apr 2026 - 22:16

score 181 · Answer 2 · 2026-05-11 02:40:50

181

Views

Which classes of subsets are absolute under forcing?

Published on 11 May 2026 - 2:40

score 54 · Answer 3 · 2026-04-15 16:26:54

54

Views

$\bigcup_{x\in K}B'(x,r)=\left \{x\in X |d(x,K)\leq r\right \}$ for $K$ compact

Published on 15 Apr 2026 - 16:26

score 217 · Answer 4 · 2026-04-09 10:48:18

217

Views

Does adding a continuous inequality constraint over a compact set lead to another compact set?

Published on 09 Apr 2026 - 10:48

score 56 · Answer 5 · 2026-05-10 16:30:13

56

Views

Altering separable space's definition

Published on 10 May 2026 - 16:30

score 130 · Answer 6 · 2026-04-13 05:21:24

Is this interior-closure identity true? $(C\cap \mathrm{Cl}(A))\cup(C\cap \mathrm{Cl}(X\setminus A))=C\cup (C\cap\partial A)$

score 202 · Answer 7 · 2026-05-13 12:49:30

202

Views

Lower limit topology and empty set

Published on 13 May 2026 - 12:49

score 51 · Answer 8 · 2026-04-11 13:27:41

51

Views

Are segments in a Partially ordered space closed/open?

Published on 11 Apr 2026 - 13:27

score 4.5k · Answer 9 · 2026-04-12 18:49:54

4.5k

Views

Prove that $A$ is open if and only if $A=\operatorname{int}{A}$

Published on 12 Apr 2026 - 18:49

score 272 · Answer 10 · 2026-04-12 04:52:35

272

Views

Is there an embedding theorem for non-second-countable manifolds?

Published on 12 Apr 2026 - 4:52

score 34 · Answer 11 · 2026-04-12 13:28:44

34

Views

Why this topological space is compact?

Published on 12 Apr 2026 - 13:28

score 139 · Answer 12 · 2026-05-11 09:57:49

139

Views

Are there more intuitive and/or illustrative reason for why covering maps do not compose besides the classical counterexample?

Published on 11 May 2026 - 9:57

score 121 · Answer 13 · 2026-04-15 12:25:14

121

Views

Strategy to prove a set is compact. Case: $S=\{0\}\cup\bigcup_\limits{i=1}^{\infty}\{\frac{1}{n}\}$

Published on 15 Apr 2026 - 12:25

score 87 · Answer 14 · 2026-05-10 15:41:52

87

Views

How to generalize transversality condition?

Published on 10 May 2026 - 15:41

score 801 · Answer 15 · 2026-04-13 05:11:02

801

Views

Is an inclusion always an homeomorphism?

Published on 13 Apr 2026 - 5:11

List Question

Exist a norm such that $S= \{x= (x_{1},x_{2}) \in R^{2}| \|x\| \leq 1, x_{2} >0\}$ which isn't open nor closed?

Which classes of subsets are absolute under forcing?

$\bigcup_{x\in K}B'(x,r)=\left \{x\in X |d(x,K)\leq r\right \}$ for $K$ compact

Does adding a continuous inequality constraint over a compact set lead to another compact set?

Altering separable space's definition

Is this interior-closure identity true? $(C\cap \mathrm{Cl}(A))\cup(C\cap \mathrm{Cl}(X\setminus A))=C\cup (C\cap\partial A)$

Lower limit topology and empty set

Are segments in a Partially ordered space closed/open?

Prove that $A$ is open if and only if $A=\operatorname{int}{A}$

Is there an embedding theorem for non-second-countable manifolds?

Why this topological space is compact?

Are there more intuitive and/or illustrative reason for why covering maps do not compose besides the classical counterexample?

Strategy to prove a set is compact. Case: $S=\{0\}\cup\bigcup_\limits{i=1}^{\infty}\{\frac{1}{n}\}$

How to generalize transversality condition?

Is an inclusion always an homeomorphism?

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