Question

Prove that for $W$ is closed vector subspace of $V$, $V/W\cong W^\perp$ as well as $V^/W^\perp\cong W^$ by a different method

score 226 · Answer 1 · 2021-03-01 15:07:48

226

Views

Prove that for $W$ is closed vector subspace of $V$, $V/W\cong W^\perp$ as well as $V^/W^\perp\cong W^$ by a different method

Published on 01 Mar 2021 - 15:07

score 237 · Answer 2 · 2021-03-02 06:08:37

237

Views

Show that the quotient norms fail to be a norm in the quotient space $\ell^{\infty}/c_{00}$.

Published on 02 Mar 2021 - 6:08

score 811 · Answer 3 · 2021-03-02 06:22:17

811

Views

Show that $V/W$ is a Banach space when $V$ is a Banach space and $W$ is a closed linear subspace.

Published on 02 Mar 2021 - 6:22

score 292 · Answer 4 · 2026-03-28 22:30:00

292

Views

Prove that Y is Hausdorff iff X is Hausdorff and A is a closed subset of X

Published on 28 Mar 2026 - 22:30

score 123 · Answer 5 · 2026-03-29 03:28:08

123

Views

Quotient of completely regular space that is not completely regular

Published on 29 Mar 2026 - 3:28

score 122 · Answer 6 · 2021-03-08 04:29:13

122

Views

Dimension of Example Quotient Space

Published on 08 Mar 2021 - 4:29

score 129 · Answer 7 · 2026-03-30 04:55:02

129

Views

Some simple questions regarding Modular Spaces, Modular Forms, Hyperbolic Geometry, Projective Special Linear and Modular Groups

Published on 30 Mar 2026 - 4:55

score 92 · Answer 8 · 2021-03-09 05:53:23

92

Views

$\mathbb{R}/{\sim}$ is Frechet Urysohn, where $x \sim y \Leftrightarrow x = y \lor x,y \in \mathbb{Z}$

Published on 09 Mar 2021 - 5:53

score 49 · Answer 9 · 2021-03-09 13:01:50

49

Views

Tensor algebra mod by an ideal

Published on 09 Mar 2021 - 13:01

score 165 · Answer 10 · 2026-03-28 22:31:09

165

Views

Find a Quotient of Hausdorff spaces not is Hausdorff

Published on 28 Mar 2026 - 22:31

score 77 · Answer 11 · 2026-03-27 12:03:11

77

Views

If $X$ is compact and space $X{/}K$ the contraction of $K$ to a point.Prove that $X{/}K$ is the compactification of $X-K$

Published on 27 Mar 2026 - 12:03

score 92 · Answer 12 · 2021-03-15 01:40:38

92

Views

About the meaning of identification space

Published on 15 Mar 2021 - 1:40

score 407 · Answer 13 · 2026-03-29 15:02:30

407

Views

Using quotient to show that a map $\mathbb{RP}^2\rightarrow\mathbb{R}^3$ is an immersion at all but six points

Published on 29 Mar 2026 - 15:02

score 140 · Answer 14 · 2026-03-30 06:48:38

140

Views

About quotient spaces of dual spaces

Published on 30 Mar 2026 - 6:48

score 65 · Answer 15 · 2021-03-20 17:05:46

65

Views

Finding inverse in a quotient ring

Published on 20 Mar 2021 - 17:05

List Question

Prove that for $W$ is closed vector subspace of $V$, $V/W\cong W^\perp$ as well as $V^/W^\perp\cong W^$ by a different method

Show that the quotient norms fail to be a norm in the quotient space $\ell^{\infty}/c_{00}$.

Show that $V/W$ is a Banach space when $V$ is a Banach space and $W$ is a closed linear subspace.

Prove that Y is Hausdorff iff X is Hausdorff and A is a closed subset of X

Quotient of completely regular space that is not completely regular

Dimension of Example Quotient Space

Some simple questions regarding Modular Spaces, Modular Forms, Hyperbolic Geometry, Projective Special Linear and Modular Groups

$\mathbb{R}/{\sim}$ is Frechet Urysohn, where $x \sim y \Leftrightarrow x = y \lor x,y \in \mathbb{Z}$

Tensor algebra mod by an ideal

Find a Quotient of Hausdorff spaces not is Hausdorff

If $X$ is compact and space $X{/}K$ the contraction of $K$ to a point.Prove that $X{/}K$ is the compactification of $X-K$

About the meaning of identification space

Using quotient to show that a map $\mathbb{RP}^2\rightarrow\mathbb{R}^3$ is an immersion at all but six points

About quotient spaces of dual spaces

Finding inverse in a quotient ring

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