Question

Open mapping theorem can fail if codomain is not Banach

score 470 · Answer 1 · 2020-08-16 18:14:45

470

Views

Open mapping theorem can fail if codomain is not Banach

Published on 16 Aug 2020 - 18:14

score 304 · Answer 2 · 2020-08-18 06:26:02

304

Views

Showing a normed vector space is the direct sum of a closed subspace and a one dimensional subspace.

Published on 18 Aug 2020 - 6:26

score 107 · Answer 3 · 2020-08-31 08:42:14

107

Views

How to show that $f'(z) \neq 0,$ for all $z \in G\ $?

Published on 31 Aug 2020 - 8:42

score 181 · Answer 4 · 2020-09-02 02:46:35

181

Views

Applying the Open Mapping Theorem

Published on 02 Sep 2020 - 2:46

score 66 · Answer 5 · 2020-09-14 10:15:47

66

Views

An application of bounded inverse theorem

Published on 14 Sep 2020 - 10:15

score 573 · Answer 6 · 2026-03-25 23:51:02

573

Views

Closed but not continuous operator

Published on 25 Mar 2026 - 23:51

score 336 · Answer 7 · 2020-09-19 12:30:46

336

Views

The exponential map exp$: \mathbb{C}\rightarrow\mathbb{C}^* = \mathbb{C}\backslash\{0\}$ is open.

Published on 19 Sep 2020 - 12:30

score 87 · Answer 8 · 2020-09-22 02:58:57

87

Views

Showing the multiplication in $\mathbb{R}$ is open

Published on 22 Sep 2020 - 2:58

score 1k · Answer 9 · 2020-09-22 15:17:34

1k

Views

Show that $f$ is continuous if and only if for every $B ∈ S_Y$ , the set $f^{−1}(B)$ is open in $X$.

Published on 22 Sep 2020 - 15:17

score 1k · Answer 10 · 2020-09-24 08:46:46

1k

Views

Show that a function is continuous if and only if for every $B ∈ S_Y$ , the set $f^{−1}(B)$ is open in $X$.

Published on 24 Sep 2020 - 8:46

score 113 · Answer 11 · 2020-09-25 00:08:23

113

Views

Does there exist a continuous bijection which is open but not closed?

Published on 25 Sep 2020 - 0:08

score 24 · Answer 12 · 2020-09-29 11:51:17

24

Views

Open mapping thm linear spaces Lemma

Published on 29 Sep 2020 - 11:51

score 58 · Answer 13 · 2020-10-11 14:37:01

58

Views

Given that $d_1$ and $d_2$ are metrics at $X$ and there are $m, M> 0$ so that $md_1 (x, y) ≤ d_2 (x, y) ≤ Md_1(x, y)$ for each $x, y \in X$

Published on 11 Oct 2020 - 14:37

score 74 · Answer 14 · 2020-10-12 02:21:17

74

Views

The map $f : \mathbb{R}^{n+1} \setminus \{0\} \to S^n$ defined by $f(x) = \frac{x}{\|x\|}$ is an open map

Published on 12 Oct 2020 - 2:21

score 287 · Answer 15 · 2020-10-23 10:39:29

287

Views

Is $f(t)=(\cos(2\pi t),\sin(2\pi t))$ an open function?

Published on 23 Oct 2020 - 10:39

List Question

Open mapping theorem can fail if codomain is not Banach

Showing a normed vector space is the direct sum of a closed subspace and a one dimensional subspace.

How to show that $f'(z) \neq 0,$ for all $z \in G\ $?

Applying the Open Mapping Theorem

An application of bounded inverse theorem

Closed but not continuous operator

The exponential map exp$: \mathbb{C}\rightarrow\mathbb{C}^* = \mathbb{C}\backslash\{0\}$ is open.

Showing the multiplication in $\mathbb{R}$ is open

Show that $f$ is continuous if and only if for every $B ∈ S_Y$ , the set $f^{−1}(B)$ is open in $X$.

Show that a function is continuous if and only if for every $B ∈ S_Y$ , the set $f^{−1}(B)$ is open in $X$.

Does there exist a continuous bijection which is open but not closed?

Open mapping thm linear spaces Lemma

Given that $d_1$ and $d_2$ are metrics at $X$ and there are $m, M> 0$ so that $md_1 (x, y) ≤ d_2 (x, y) ≤ Md_1(x, y)$ for each $x, y \in X$

The map $f : \mathbb{R}^{n+1} \setminus \{0\} \to S^n$ defined by $f(x) = \frac{x}{\|x\|}$ is an open map

Is $f(t)=(\cos(2\pi t),\sin(2\pi t))$ an open function?

Trending Questions

Popular # Hahtags

Popular Questions