Question

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

score 87 · Answer 1 · 2018-01-28 23:06:49

87

Views

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Published on 28 Jan 2018 - 23:06

score 662 · Answer 2 · 2026-03-23 04:43:33

662

Views

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

Published on 23 Mar 2026 - 4:43

score 70 · Answer 3 · 2018-01-29 00:13:26

70

Views

Question About Cantor's Intersection Theorem

Published on 29 Jan 2018 - 0:13

score 60 · Answer 4 · 2026-03-25 11:10:08

60

Views

Necessary and sufficient condition: continuous map on semi-normed vector spaces

Published on 25 Mar 2026 - 11:10

score 63 · Answer 5 · 2026-03-26 12:07:07

63

Views

Proving $D := \{ \ (x,y) \in \mathbb{R^2} \ \mid \ 1+x^2+y > 0 \ \}$ is open

Published on 26 Mar 2026 - 12:07

score 1.4k · Answer 6 · 2026-03-19 16:07:31

1.4k

Views

Unit ball in dual space is weak*separable

Published on 19 Mar 2026 - 16:07

score 177 · Answer 7 · 2018-01-29 15:10:10

177

Views

Is the continuity of measures a topological continuity?

Published on 29 Jan 2018 - 15:10

score 208 · Answer 8 · 2026-03-20 10:25:03

208

Views

Non-contractible simplicial complex and Euler characteristic 1

Published on 20 Mar 2026 - 10:25

score 66 · Answer 9 · 2026-03-19 20:40:28

66

Views

Fixed point of a map $\mathbb R^n \rightarrow \mathbb R^n$

Published on 19 Mar 2026 - 20:40

score 1.1k · Answer 10 · 2018-01-29 17:38:52

1.1k

Views

Are all the $\ell^p$ metrics topologically equivalent for positive integer values of $p$?

Published on 29 Jan 2018 - 17:38

score 234 · Answer 11 · 2026-03-26 05:38:02

Proving that $[0,1] \times X \cong [0,1] \times Y$, where $X$ is Möbius strip, $Y$ is curved surface of cylinder, and $\cong$ denotes homeomorphic

score 63 · Answer 12 · 2026-03-25 04:43:22

63

Views

On the topological properties and measure of $\{(A,B)\in M(n,\mathbb R)\times M(n,\mathbb R) : \det (A+B)=\det(A)+\det(B)\}$

Published on 25 Mar 2026 - 4:43

score 498 · Answer 13 · 2018-01-29 21:22:16

498

Views

Show that every open set A in a metric space (X, d) is the union of closed sets.

Published on 29 Jan 2018 - 21:22

score 398 · Answer 14 · 2018-01-29 21:35:02

398

Views

Relative topology theorem hunt.

Published on 29 Jan 2018 - 21:35

score 62 · Answer 15 · 2018-01-30 04:32:22

62

Views

Show that $E$ is the closure of $A$.

Published on 30 Jan 2018 - 4:32

List Question

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

Question About Cantor's Intersection Theorem

Necessary and sufficient condition: continuous map on semi-normed vector spaces

Proving $D := \{ \ (x,y) \in \mathbb{R^2} \ \mid \ 1+x^2+y > 0 \ \}$ is open

Unit ball in dual space is weak*separable

Is the continuity of measures a topological continuity?

Non-contractible simplicial complex and Euler characteristic 1

Fixed point of a map $\mathbb R^n \rightarrow \mathbb R^n$

Are all the $\ell^p$ metrics topologically equivalent for positive integer values of $p$?

Proving that $[0,1] \times X \cong [0,1] \times Y$, where $X$ is Möbius strip, $Y$ is curved surface of cylinder, and $\cong$ denotes homeomorphic

On the topological properties and measure of $\{(A,B)\in M(n,\mathbb R)\times M(n,\mathbb R) : \det (A+B)=\det(A)+\det(B)\}$

Show that every open set A in a metric space (X, d) is the union of closed sets.

Relative topology theorem hunt.

Show that $E$ is the closure of $A$.

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