Question

Natural topology on a particular subset of the set of continuous maps from $[0,1]^n$ to $\mathbb{R}$

score 28 · Answer 1 · 2020-11-14 13:35:27

28

Views

Natural topology on a particular subset of the set of continuous maps from $[0,1]^n$ to $\mathbb{R}$

Published on 14 Nov 2020 - 13:35

score 106 · Answer 2 · 2020-11-23 21:40:48

106

Views

What does the norm tell me in this function space?

Published on 23 Nov 2020 - 21:40

score 163 · Answer 3 · 2020-12-15 09:12:34

163

Views

Interprete Banach spaces as subspace of the space of continuous functions on a compact space

Published on 15 Dec 2020 - 9:12

score 153 · Answer 4 · 2020-12-26 13:05:10

153

Views

$\Phi: X \to \mathscr F (J,Y)$ is continuous $\iff$ $\forall j\in J$ we have that $X\to Y$ given by $x \mapsto (\Phi(x))(j)$ is continuous.

Published on 26 Dec 2020 - 13:05

score 108 · Answer 5 · 2021-01-01 08:33:55

108

Views

Function space, Harmonic analysis

Published on 01 Jan 2021 - 8:33

score 34 · Answer 6 · 2021-01-15 04:38:57

34

Views

Arbitrarily dilated Triebel-Lizorkin space have equivalence with original Triebel-Lizorkin space?

Published on 15 Jan 2021 - 4:38

score 40 · Answer 7 · 2021-02-01 06:29:58

40

Views

Where can I find literature regarding cardinal invariants of a function space C(X,Y) endowed with the Uniform or Fine topology?

Published on 01 Feb 2021 - 6:29

score 74 · Answer 8 · 2021-02-07 14:02:31

74

Views

Non-Metrizability of Compact-Open Topology

Published on 07 Feb 2021 - 14:02

score 37 · Answer 9 · 2021-02-25 05:14:25

37

Views

How can we prove for a tychonoff space $X$ and a metric space $(Y, d)$, that a map $\phi : Y \rightarrow C(X, Y)$, is an embedding.

Published on 25 Feb 2021 - 5:14

score 283 · Answer 10 · 2021-02-25 09:40:17

283

Views

Showing that the derivative function is not continuous w.r.t. the sup norm

Published on 25 Feb 2021 - 9:40

score 69 · Answer 11 · 2021-02-26 03:47:16

69

Views

What are some examples of algebras that satisfy the hypothesis of Stone's theorem?

Published on 26 Feb 2021 - 3:47

score 50 · Answer 12 · 2021-02-27 22:59:02

50

Views

Graph structure on graph homomorphisms

Published on 27 Feb 2021 - 22:59

score 134 · Answer 13 · 2021-03-02 10:08:01

134

Views

How to prove that a tychonoff space $C(X, Y)$ equipped with fine topology can be embedded in a tychonoff cube.

Published on 02 Mar 2021 - 10:08

score 76 · Answer 14 · 2021-03-04 05:11:23

76

Views

How can one the cardinality of function space $C(X, Y)$ equipped with uniform topology, where $X$ is a Tychonoff space and $(Y, d)$ a metric space.

Published on 04 Mar 2021 - 5:11

score 28 · Answer 15 · 2021-03-07 07:25:31

28

Views

Can we define a reverse mapping for the $\phi : Y \rightarrow C(X, Y)$, as $\phi(y) = y' $, where $y' $ is a constant map in $C(X, Y)$.

Published on 07 Mar 2021 - 7:25

List Question

Natural topology on a particular subset of the set of continuous maps from $[0,1]^n$ to $\mathbb{R}$

What does the norm tell me in this function space?

Interprete Banach spaces as subspace of the space of continuous functions on a compact space

$\Phi: X \to \mathscr F (J,Y)$ is continuous $\iff$ $\forall j\in J$ we have that $X\to Y$ given by $x \mapsto (\Phi(x))(j)$ is continuous.

Function space, Harmonic analysis

Arbitrarily dilated Triebel-Lizorkin space have equivalence with original Triebel-Lizorkin space?

Where can I find literature regarding cardinal invariants of a function space C(X,Y) endowed with the Uniform or Fine topology?

Non-Metrizability of Compact-Open Topology

How can we prove for a tychonoff space $X$ and a metric space $(Y, d)$, that a map $\phi : Y \rightarrow C(X, Y)$, is an embedding.

Showing that the derivative function is not continuous w.r.t. the sup norm

What are some examples of algebras that satisfy the hypothesis of Stone's theorem?

Graph structure on graph homomorphisms

How to prove that a tychonoff space $C(X, Y)$ equipped with fine topology can be embedded in a tychonoff cube.

How can one the cardinality of function space $C(X, Y)$ equipped with uniform topology, where $X$ is a Tychonoff space and $(Y, d)$ a metric space.

Can we define a reverse mapping for the $\phi : Y \rightarrow C(X, Y)$, as $\phi(y) = y' $, where $y' $ is a constant map in $C(X, Y)$.

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