Question

$(a,b)$ is polish space with induced topology

score 181 · Answer 1 · 2026-02-23 08:39:36

181

Views

$(a,b)$ is polish space with induced topology

Published on 23 Feb 2026 - 8:39

score 82 · Answer 2 · 2021-03-19 21:26:56

82

Views

Uniform Convergence of $f_n(x) = \frac{n(1-2x) + \cos x -x\sin^2 x}{2n + \sin^2 x}$ [proof verification]

Published on 19 Mar 2021 - 21:26

score 74 · Answer 3 · 2021-03-19 22:00:30

74

Views

Proving that a sequence does not converge?

Published on 19 Mar 2021 - 22:00

score 172 · Answer 4 · 2021-03-24 13:42:37

172

Views

why do we need to prove that the limit of a contraction is a fixed point in the contraction mapping theorem

Published on 24 Mar 2021 - 13:42

score 81 · Answer 5 · 2026-03-30 00:03:45

81

Views

Why is the unitization of $M_\infty(\mathbb{C})$ not complete?

Published on 30 Mar 2026 - 0:03

score 191 · Answer 6 · 2021-03-25 21:15:22

191

Views

Prove that the sequence $(x_n)$ is Cauchy.

Published on 25 Mar 2021 - 21:15

score 32 · Answer 7 · 2021-03-27 07:07:55

32

Views

If $\vert \vert x_{k+1} - a \vert \vert \leq c \vert \vert x_k-a \vert \vert$, $c \in [0,1)$ then $ \lim x_k = a$

Published on 27 Mar 2021 - 7:07

score 854 · Answer 8 · 2026-03-29 23:58:22

854

Views

Space of bounded functions is complete

Published on 29 Mar 2026 - 23:58

score 59 · Answer 9 · 2021-03-29 15:12:25

59

Views

Let $(x_n)$ be a Cauchy sequence in $(X,d)$ and $a \in X$. Show that there exist $M>0$ such that $x_n \in B(a,M)$ for all $n \in \mathbb{N}$.

Published on 29 Mar 2021 - 15:12

score 282 · Answer 10 · 2021-03-30 18:30:56

282

Views

How can a sequence be Cauchy and divergent at the same time?

Published on 30 Mar 2021 - 18:30

score 94 · Answer 11 · 2021-04-03 17:06:53

94

Views

Show $\lim{\frac{1}{\sqrt{n+1}}+\frac{1}{\sqrt{n+2}}+\frac{1}{\sqrt{n+3}}+...\frac{1}{\sqrt{2n}}}=\infty$

Published on 03 Apr 2021 - 17:06

score 191 · Answer 12 · 2021-04-04 22:33:27

191

Views

$K_n \supseteq K_{n+1}$, $K_n \neq \emptyset$, $K_n$ is compact, $\text{diam}(K_n)\to 0$ implies $\bigcap_{n=1}^{\infty} K_n = \{x\}$

Published on 04 Apr 2021 - 22:33

score 31 · Answer 13 · 2021-04-05 05:04:13

31

Views

Show that a the uniform metric over the set of bounded functions is complete

Published on 05 Apr 2021 - 5:04

score 69 · Answer 14 · 2021-04-07 18:03:25

69

Views

Cauchy Sequence and Continuity of function

Published on 07 Apr 2021 - 18:03

score 40 · Answer 15 · 2021-04-08 05:15:30

40

Views

Test whether the recurence sequence is convergent

Published on 08 Apr 2021 - 5:15

List Question

$(a,b)$ is polish space with induced topology

Uniform Convergence of $f_n(x) = \frac{n(1-2x) + \cos x -x\sin^2 x}{2n + \sin^2 x}$ [proof verification]

Proving that a sequence does not converge?

why do we need to prove that the limit of a contraction is a fixed point in the contraction mapping theorem

Why is the unitization of $M_\infty(\mathbb{C})$ not complete?

Prove that the sequence $(x_n)$ is Cauchy.

If $\vert \vert x_{k+1} - a \vert \vert \leq c \vert \vert x_k-a \vert \vert$, $c \in [0,1)$ then $ \lim x_k = a$

Space of bounded functions is complete

Let $(x_n)$ be a Cauchy sequence in $(X,d)$ and $a \in X$. Show that there exist $M>0$ such that $x_n \in B(a,M)$ for all $n \in \mathbb{N}$.

How can a sequence be Cauchy and divergent at the same time?

Show $\lim{\frac{1}{\sqrt{n+1}}+\frac{1}{\sqrt{n+2}}+\frac{1}{\sqrt{n+3}}+...\frac{1}{\sqrt{2n}}}=\infty$

$K_n \supseteq K_{n+1}$, $K_n \neq \emptyset$, $K_n$ is compact, $\text{diam}(K_n)\to 0$ implies $\bigcap_{n=1}^{\infty} K_n = \{x\}$

Show that a the uniform metric over the set of bounded functions is complete

Cauchy Sequence and Continuity of function

Test whether the recurence sequence is convergent

Trending Questions

Popular # Hahtags

Popular Questions