Question

Open Mapping Theorem and the Bounded Inverse Theorem to show $T^{-1}$ is not bounded

score 67 · Answer 1 · 2021-12-01 13:34:24

67

Views

Open Mapping Theorem and the Bounded Inverse Theorem to show $T^{-1}$ is not bounded

Published on 01 Dec 2021 - 13:34

score 102 · Answer 2 · 2021-12-07 22:00:36

102

Views

How far is this view correct on strengthening and weakening of the topologies of the domain and the codomain?

Published on 07 Dec 2021 - 22:00

score 43 · Answer 3 · 2021-12-11 02:52:54

43

Views

Let $ \Omega _1, \Omega _2$ be domains and let $f:\Omega _1\rightarrow \Omega _2$ be biholomorphism. Is this $f$ an open function?

Published on 11 Dec 2021 - 2:52

score 67 · Answer 4 · 2022-01-11 15:45:09

67

Views

Show that $\dim(Z) < \infty$ if $Z \subset T(X)$ for compact $T$

Published on 11 Jan 2022 - 15:45

score 74 · Answer 5 · 2022-01-13 15:15:54

74

Views

How the author obtains $\|x\| < 1$ in this proof of open mapping theorem?

Published on 13 Jan 2022 - 15:15

score 45 · Answer 6 · 2026-03-26 01:23:42

45

Views

If $U \subset Y \subset \mathbb{R}^n$, and $U$ is open relative to $Y$, then is $\Pi_k(U)$ open relative to $\Pi_k(Y)$? ($\Pi_k$ is a projection map)

Published on 26 Mar 2026 - 1:23

score 134 · Answer 7 · 2022-02-02 12:49:45

134

Views

Why do we need Poincaré inequality to deduce the equivalence of the norms $\|\cdot\|_{H^1_0}$ and $\|\cdot\|_{H^1}$ on $H^1_0(\Omega)$?

Published on 02 Feb 2022 - 12:49

score 128 · Answer 8 · 2026-03-26 08:04:29

128

Views

An example of a closed quotient map that is not open

Published on 26 Mar 2026 - 8:04

score 61 · Answer 9 · 2022-03-10 20:47:26

61

Views

Graphing $f(x) = x(-1)^x$ on $\mathbb{R}$

Published on 10 Mar 2022 - 20:47

score 42 · Answer 10 · 2022-03-14 20:33:17

42

Views

Topology Counterexample - Book Error?: Prove: Let f:(X, T) -> (Y, T) be open and onto, and let B be a Base for T. Show f(B) is a base for T

Published on 14 Mar 2022 - 20:33

score 111 · Answer 11 · 2022-03-31 23:39:35

111

Views

Proving that the component spaces are connected if the product space is connected

Published on 31 Mar 2022 - 23:39

score 180 · Answer 12 · 2022-04-04 10:01:25

180

Views

Open mapping, inverse mapping and boundness

Published on 04 Apr 2022 - 10:01

score 149 · Answer 13 · 2022-04-09 22:59:19

149

Views

Is $e^{itA}$ an open map?

Published on 09 Apr 2022 - 22:59

score 79 · Answer 14 · 2022-04-29 04:43:21

79

Views

Can an injective contraction take a set with nonempty interior to one with empty interior?

Published on 29 Apr 2022 - 4:43

score 60 · Answer 15 · 2026-03-26 14:43:22

60

Views

Application of the open function theorem (BANACH) with $f\not\equiv 0$.

Published on 26 Mar 2026 - 14:43

List Question

Open Mapping Theorem and the Bounded Inverse Theorem to show $T^{-1}$ is not bounded

How far is this view correct on strengthening and weakening of the topologies of the domain and the codomain?

Let $ \Omega _1, \Omega _2$ be domains and let $f:\Omega _1\rightarrow \Omega _2$ be biholomorphism. Is this $f$ an open function?

Show that $\dim(Z) < \infty$ if $Z \subset T(X)$ for compact $T$

How the author obtains $\|x\| < 1$ in this proof of open mapping theorem?

If $U \subset Y \subset \mathbb{R}^n$, and $U$ is open relative to $Y$, then is $\Pi_k(U)$ open relative to $\Pi_k(Y)$? ($\Pi_k$ is a projection map)

Why do we need Poincaré inequality to deduce the equivalence of the norms $\|\cdot\|_{H^1_0}$ and $\|\cdot\|_{H^1}$ on $H^1_0(\Omega)$?

An example of a closed quotient map that is not open

Graphing $f(x) = x(-1)^x$ on $\mathbb{R}$

Topology Counterexample - Book Error?: Prove: Let f:(X, T) -> (Y, T) be open and onto, and let B be a Base for T. Show f(B) is a base for T

Proving that the component spaces are connected if the product space is connected

Open mapping, inverse mapping and boundness

Is $e^{itA}$ an open map?

Can an injective contraction take a set with nonempty interior to one with empty interior?

Application of the open function theorem (BANACH) with $f\not\equiv 0$.

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