Question

complete metric space and unique fixed point

score 239 · Answer 1 · 2018-03-07 15:56:11

239

Views

complete metric space and unique fixed point

Published on 07 Mar 2018 - 15:56

score 584 · Answer 2 · 2026-03-25 06:04:47

584

Views

What does a nonsymmetric connection on $\Bbb R^n$ look like?

Published on 25 Mar 2026 - 6:04

score 149 · Answer 3 · 2026-03-24 22:07:40

149

Views

To deduce that neither of the metric spaces $(\mathbb{R}^n, d_1)$ and $(\mathbb{R}^n, d_{\infty})$ is isometric to $(\mathbb{R}^n, d_2)$.

Published on 24 Mar 2026 - 22:07

score 140 · Answer 4 · 2026-03-30 03:11:00

140

Views

To check that under a constructed complete metric on $(0,1)$ the sequence $1/n$ is not cauchy

Published on 30 Mar 2026 - 3:11

score 1.6k · Answer 5 · 2026-03-25 15:11:10

1.6k

Views

Showing that a connected set is a connected component

Published on 25 Mar 2026 - 15:11

score 36 · Answer 6 · 2018-03-08 18:38:59

36

Views

Continuity and close map . [Metric Space.]

Published on 08 Mar 2018 - 18:38

score 450 · Answer 7 · 2026-03-25 16:40:13

450

Views

Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

Published on 25 Mar 2026 - 16:40

score 68 · Answer 8 · 2018-03-08 21:11:46

68

Views

Metric Space (Continuity)

Published on 08 Mar 2018 - 21:11

score 290 · Answer 9 · 2026-03-24 23:44:24

290

Views

Show this function is not cauchy in the metric space?

Published on 24 Mar 2026 - 23:44

score 61 · Answer 10 · 2026-03-27 00:06:02

61

Views

Prove that the set $Y = \{f \in C[0, 2] \ | \ f(1) = 0 \} \subseteq (C[0, 2], d)$ where $d$ is the uniform metric is closed.

Published on 27 Mar 2026 - 0:06

score 580 · Answer 11 · 2026-03-24 22:51:09

580

Views

affine functions and Lipschitz continuity

Published on 24 Mar 2026 - 22:51

score 59 · Answer 12 · 2018-03-10 11:32:10

59

Views

If f:X→R is a continuous non constant function and X is connected then X is uncountable.

Published on 10 Mar 2018 - 11:32

score 57 · Answer 13 · 2018-03-10 11:39:06

57

Views

Prove that $u(x)-u(y) \le d(x,y) \le u(x)+u(y)$

Published on 10 Mar 2018 - 11:39

score 289 · Answer 14 · 2026-03-26 01:23:37

289

Views

Any open neighborhood of a boundary point contains an interior point and an exterior point.

Published on 26 Mar 2026 - 1:23

score 50 · Answer 15 · 2018-03-10 18:07:11

There exists a function $f: \Bbb R \mapsto \Bbb R$ such that $f^{(4)}(x)$ exists for all $x$ in $\Bbb R$ but is discontinuous at $x=0$

List Question

complete metric space and unique fixed point

What does a nonsymmetric connection on $\Bbb R^n$ look like?

To deduce that neither of the metric spaces $(\mathbb{R}^n, d_1)$ and $(\mathbb{R}^n, d_{\infty})$ is isometric to $(\mathbb{R}^n, d_2)$.

To check that under a constructed complete metric on $(0,1)$ the sequence $1/n$ is not cauchy

Showing that a connected set is a connected component

Continuity and close map . [Metric Space.]

Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

Metric Space (Continuity)

Show this function is not cauchy in the metric space?

Prove that the set $Y = \{f \in C[0, 2] \ | \ f(1) = 0 \} \subseteq (C[0, 2], d)$ where $d$ is the uniform metric is closed.

affine functions and Lipschitz continuity

If f:X→R is a continuous non constant function and X is connected then X is uncountable.

Prove that $u(x)-u(y) \le d(x,y) \le u(x)+u(y)$

Any open neighborhood of a boundary point contains an interior point and an exterior point.

There exists a function $f: \Bbb R \mapsto \Bbb R$ such that $f^{(4)}(x)$ exists for all $x$ in $\Bbb R$ but is discontinuous at $x=0$

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