Question

For $f:X\rightarrow Y,$ if $f$ is continuous and $X$ is a complete metric space, does $f$ preserve Cauchy sequences?

score 718 · Answer 1 · 2017-04-22 04:59:08

718

Views

For $f:X\rightarrow Y,$ if $f$ is continuous and $X$ is a complete metric space, does $f$ preserve Cauchy sequences?

Published on 22 Apr 2017 - 4:59

score 57 · Answer 2 · 2017-04-22 18:22:25

57

Views

How to pick $N$ for Cauchy sequence?

Published on 22 Apr 2017 - 18:22

score 30 · Answer 3 · 2017-04-23 21:28:46

30

Views

Find all values of $r \ge 0$ such that $x_n = \frac{r^n}{r^n + 1}$ is Cauchy.

Published on 23 Apr 2017 - 21:28

score 74 · Answer 4 · 2017-04-24 20:08:02

74

Views

Constructing a special kind of sequence in an infinite dimensional normed linear space

Published on 24 Apr 2017 - 20:08

score 487 · Answer 5 · 2017-04-25 06:35:44

487

Views

An application of Open Mapping Theorem and Quotient map

Published on 25 Apr 2017 - 6:35

score 767 · Answer 6 · 2017-04-27 13:07:57

767

Views

If $\lim_{n \rightarrow \infty} (a_{n+1}-\frac{a_n}{2})=0$ then show $a_n$ converges to $0$.

Published on 27 Apr 2017 - 13:07

score 186 · Answer 7 · 2026-03-28 12:14:18

186

Views

Show that $(a_k)$ is a Cauchy sequence in this metric space

Published on 28 Mar 2026 - 12:14

score 62 · Answer 8 · 2026-04-03 02:59:01

62

Views

Is $f(x)=\frac{1}{x-3}$ not uniformly continuous on $(3,\infty)$?

Published on 03 Apr 2026 - 2:59

score 207 · Answer 9 · 2026-03-30 17:06:31

207

Views

Lipschitz conditions proof

Published on 30 Mar 2026 - 17:06

score 1.6k · Answer 10 · 2017-05-01 01:51:31

1.6k

Views

The real line equipped with the distance $p(x,y)= |\arctan (x)-\arctan (y)|$ is an incomplete metric space.

Published on 01 May 2017 - 1:51

score 153 · Answer 11 · 2017-05-01 22:53:38

153

Views

Show that Cauchy sequence $(a_k)$ isn't d-convergent in the set of eventually zero sequences

Published on 01 May 2017 - 22:53

score 161 · Answer 12 · 2017-05-02 17:00:41

161

Views

Prove L $\in$ [a, b]

Published on 02 May 2017 - 17:00

score 217 · Answer 13 · 2017-05-03 01:17:06

217

Views

"Convex" sequence converges?

Published on 03 May 2017 - 1:17

score 303 · Answer 14 · 2017-05-03 21:28:55

303

Views

Define $S_n=f(S_{n-1})$ for $n\geq 1$. Prove $S_n$ is a convergent sequence.

Published on 03 May 2017 - 21:28

score 114 · Answer 15 · 2017-05-05 04:54:37

114

Views

Prove a sequence is cauchy if it is based on a cauchy sequence

Published on 05 May 2017 - 4:54

List Question

For $f:X\rightarrow Y,$ if $f$ is continuous and $X$ is a complete metric space, does $f$ preserve Cauchy sequences?

How to pick $N$ for Cauchy sequence?

Find all values of $r \ge 0$ such that $x_n = \frac{r^n}{r^n + 1}$ is Cauchy.

Constructing a special kind of sequence in an infinite dimensional normed linear space

An application of Open Mapping Theorem and Quotient map

If $\lim_{n \rightarrow \infty} (a_{n+1}-\frac{a_n}{2})=0$ then show $a_n$ converges to $0$.

Show that $(a_k)$ is a Cauchy sequence in this metric space

Is $f(x)=\frac{1}{x-3}$ not uniformly continuous on $(3,\infty)$?

Lipschitz conditions proof

The real line equipped with the distance $p(x,y)= |\arctan (x)-\arctan (y)|$ is an incomplete metric space.

Show that Cauchy sequence $(a_k)$ isn't d-convergent in the set of eventually zero sequences

Prove L $\in$ [a, b]

"Convex" sequence converges?

Define $S_n=f(S_{n-1})$ for $n\geq 1$. Prove $S_n$ is a convergent sequence.

Prove a sequence is cauchy if it is based on a cauchy sequence

Trending Questions

Popular # Hahtags

Popular Questions