Question

Let $f : [0,1] \to [0,1]$ continuous and $(u_n)$ s.t. $\forall n, u_{n+1}=f(u_n)$. Show that $(u_n)$ converges $\iff u_{n+1} - u_n \to 0$

score 113 · Answer 1 · 2026-04-03 20:18:33

113

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Let $f : [0,1] \to [0,1]$ continuous and $(u_n)$ s.t. $\forall n, u_{n+1}=f(u_n)$. Show that $(u_n)$ converges $\iff u_{n+1} - u_n \to 0$

Published on 03 Apr 2026 - 20:18

score 50 · Answer 2 · 2018-06-06 19:57:22

50

Views

Is the unity ball of $rba(X)$ a $G_{\delta}$ space?

Published on 06 Jun 2018 - 19:57

score 134 · Answer 3 · 2026-03-25 09:49:26

134

Views

Is the set of coefficients connected for monic polynomial with roots bounded by some interval?

Published on 25 Mar 2026 - 9:49

score 192 · Answer 4 · 2026-03-25 11:20:18

192

Views

Topological property of preimage of map $f$ taking the coefficients of characteristic polynomial?

Published on 25 Mar 2026 - 11:20

score 452 · Answer 5 · 2026-04-02 09:54:43

452

Views

The complement of image of a continuous function can not be one point in Hausdroff space

Published on 02 Apr 2026 - 9:54

score 87 · Answer 6 · 2026-03-28 10:15:00

87

Views

About a metric space

Published on 28 Mar 2026 - 10:15

score 61 · Answer 7 · 2018-06-07 14:12:00

61

Views

Consider the sequence $x_n = (7 + (-1)^n/n, -5) \in\mathbb{R^2}$. What are the sets of limit points in different topologies?

Published on 07 Jun 2018 - 14:12

score 228 · Answer 8 · 2026-03-28 15:26:08

228

Views

Proof that if $f:S^{n} \to \mathbb{R} $ is continuous, then is not injective

Published on 28 Mar 2026 - 15:26

score 181 · Answer 9 · 2026-03-25 06:28:06

181

Views

Topological shape of the color spectrum

Published on 25 Mar 2026 - 6:28

score 147 · Answer 10 · 2026-04-01 20:08:52

147

Views

Global sections functor commutes with tensor product for $\Gamma$-acyclic sheaves?

Published on 01 Apr 2026 - 20:08

score 38 · Answer 11 · 2026-03-25 13:51:50

38

Views

Is this map proper?

Published on 25 Mar 2026 - 13:51

score 301 · Answer 12 · 2018-06-07 20:49:40

301

Views

baby rudin chapter 2 problem 21(b)- help with alternative method

Published on 07 Jun 2018 - 20:49

score 73 · Answer 13 · 2026-03-28 15:01:33

73

Views

Compact and open sets

Published on 28 Mar 2026 - 15:01

score 437 · Answer 14 · 2026-03-25 00:02:55

437

Views

In $R^n,$ convex cone of any compact set is closed? cone of any compact set is closed?

Published on 25 Mar 2026 - 0:02

score 92 · Answer 15 · 2018-06-07 21:25:01

92

Views

Is the preimage of $f(x) = x_1 x_2 \dots x_n$ connected?

Published on 07 Jun 2018 - 21:25

List Question

Let $f : [0,1] \to [0,1]$ continuous and $(u_n)$ s.t. $\forall n, u_{n+1}=f(u_n)$. Show that $(u_n)$ converges $\iff u_{n+1} - u_n \to 0$

Is the unity ball of $rba(X)$ a $G_{\delta}$ space?

Is the set of coefficients connected for monic polynomial with roots bounded by some interval?

Topological property of preimage of map $f$ taking the coefficients of characteristic polynomial?

The complement of image of a continuous function can not be one point in Hausdroff space

About a metric space

Consider the sequence $x_n = (7 + (-1)^n/n, -5) \in\mathbb{R^2}$. What are the sets of limit points in different topologies?

Proof that if $f:S^{n} \to \mathbb{R} $ is continuous, then is not injective

Topological shape of the color spectrum

Global sections functor commutes with tensor product for $\Gamma$-acyclic sheaves?

Is this map proper?

baby rudin chapter 2 problem 21(b)- help with alternative method

Compact and open sets

In $R^n,$ convex cone of any compact set is closed? cone of any compact set is closed?

Is the preimage of $f(x) = x_1 x_2 \dots x_n$ connected?

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