Question

If $d_1(x,y) \leq d_2(x,y)$ and all $d_2$-closed balls in $M$ are also $d_1$-closed, then $(M,d_2)$ is complete.

score 138 · Answer 1 · 2017-04-13 01:09:13

138

Views

If $d_1(x,y) \leq d_2(x,y)$ and all $d_2$-closed balls in $M$ are also $d_1$-closed, then $(M,d_2)$ is complete.

Published on 13 Apr 2017 - 1:09

score 53 · Answer 2 · 2017-04-13 20:44:13

53

Views

Is a complete metric space a continuum?

Published on 13 Apr 2017 - 20:44

score 3.2k · Answer 3 · 2017-04-23 19:56:36

3.2k

Views

Proving that the sequence space $l^1$ is complete

Published on 23 Apr 2017 - 19:56

score 185 · Answer 4 · 2017-04-29 17:36:23

185

Views

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

Published on 29 Apr 2017 - 17:36

score 245 · Answer 5 · 2017-05-02 23:25:29

245

Views

What does it mean for a Metric to be complete?

Published on 02 May 2017 - 23:25

score 1.4k · Answer 6 · 2017-05-03 23:02:50

1.4k

Views

Existence of a vector space with two non equivalent norms, while both of them are complete

Published on 03 May 2017 - 23:02

score 998 · Answer 7 · 2017-05-05 19:13:19

998

Views

The normed vector space of continuous function is complete

Published on 05 May 2017 - 19:13

score 138 · Answer 8 · 2017-05-06 05:00:03

138

Views

Prove that $(C[0, T], ρ)$ is a complete metric space.

Published on 06 May 2017 - 5:00

score 34 · Answer 9 · 2017-05-10 06:18:43

34

Views

When we eradicate one element from a complete space, how to reach the completeness of this new space?

Published on 10 May 2017 - 6:18

score 37 · Answer 10 · 2017-05-10 22:14:29

37

Views

Embedding of a closed subspace of $L^1_m([0,1])$ with each element in some $L^p$ with $p>1$ in a higher $L^{p_0}$.

Published on 10 May 2017 - 22:14

score 306 · Answer 11 · 2017-05-11 13:14:55

306

Views

Sequences that converge to the same point

Published on 11 May 2017 - 13:14

score 53 · Answer 12 · 2017-05-11 14:29:16

53

Views

Complete subspace of connected space

Published on 11 May 2017 - 14:29

score 123 · Answer 13 · 2017-05-14 00:08:27

123

Views

Showing that $f$ under the $1$-norm is not a contraction.

Published on 14 May 2017 - 0:08

score 107 · Answer 14 · 2017-05-24 07:47:24

107

Views

Verify that any Cauchy sequence in $c_0$ (equipped with the supremum norm) converges to a limit in $c_0.$

Published on 24 May 2017 - 7:47

score 1k · Answer 15 · 2017-05-25 03:48:19

1k

Views

Show that $c_0$ is not a Banach space in the $\| \cdot \|_2$-norm.

Published on 25 May 2017 - 3:48

List Question

If $d_1(x,y) \leq d_2(x,y)$ and all $d_2$-closed balls in $M$ are also $d_1$-closed, then $(M,d_2)$ is complete.

Is a complete metric space a continuum?

Proving that the sequence space $l^1$ is complete

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

What does it mean for a Metric to be complete?

Existence of a vector space with two non equivalent norms, while both of them are complete

The normed vector space of continuous function is complete

Prove that $(C[0, T], ρ)$ is a complete metric space.

When we eradicate one element from a complete space, how to reach the completeness of this new space?

Embedding of a closed subspace of $L^1_m([0,1])$ with each element in some $L^p$ with $p>1$ in a higher $L^{p_0}$.

Sequences that converge to the same point

Complete subspace of connected space

Showing that $f$ under the $1$-norm is not a contraction.

Verify that any Cauchy sequence in $c_0$ (equipped with the supremum norm) converges to a limit in $c_0.$

Show that $c_0$ is not a Banach space in the $\| \cdot \|_2$-norm.

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