Question

Given $\varepsilon > 0$ and an irrational $\alpha$, there exists a rational number $m / n$ that is ($\varepsilon / n$)-close to $\alpha$?

score 50 · Answer 1 · 2024-01-27 20:40:55

50

Views

Given $\varepsilon > 0$ and an irrational $\alpha$, there exists a rational number $m / n$ that is ($\varepsilon / n$)-close to $\alpha$?

Published on 27 Jan 2024 - 20:40

score 73 · Answer 2 · 2024-02-03 21:38:59

73

Views

If two function agree on a dense set, what condition is necessary for them to be equal?

Published on 03 Feb 2024 - 21:38

score 66 · Answer 3 · 2024-02-12 07:23:16

66

Views

The complement of any set of first category on the line is dense iff the intersection of any sequence of dense open sets is dense

Published on 12 Feb 2024 - 7:23

score 86 · Answer 4 · 2024-02-22 14:39:04

86

Views

Necessity of Hausdorff-ness in "continuous function determined by its values on a dense subset"

Published on 22 Feb 2024 - 14:39

score 31 · Answer 5 · 2024-02-25 16:41:07

31

Views

A separable normed space that is continuously embedded in a non-separable normed space implies that this embedding isn't dense.

Published on 25 Feb 2024 - 16:41

score 80 · Answer 6 · 2024-03-03 09:24:07

80

Views

Real Polynomials on Compact sets of Complex numbers

Published on 03 Mar 2024 - 9:24

score 31 · Answer 7 · 2024-03-09 17:40:03

31

Views

Let $X$ be a normed linear space and let $V \subseteq X$ be a closed linear subspace such that $V \neq X$. Prove that $V$ is nowhere dense.

Published on 09 Mar 2024 - 17:40

score 66 · Answer 8 · 2024-03-16 13:43:37

66

Views

What is the importance of the density of $C_c^\infty(\mathbb R^n)$ and $L_c^\infty(\mathbb R^n)$ on $L^p(\mathbb R^n)$, for every $1 \leq p < \infty$?

Published on 16 Mar 2024 - 13:43

score 54 · Answer 9 · 2024-03-20 17:12:38

54

Views

Density argument in Normed spaces

Published on 20 Mar 2024 - 17:12

score 109 · Answer 10 · 2024-03-23 15:38:05

109

Views

Square integrable for universal approximation

Published on 23 Mar 2024 - 15:38

score 114 · Answer 11 · 2024-03-23 20:53:26

114

Views

Demonstrating Density Using the Stone-Weierstrass Theorem

Published on 23 Mar 2024 - 20:53

score 15 · Answer 12 · 2024-03-29 13:49:25

15

Views

Random functions and neuronal network

Published on 29 Mar 2024 - 13:49

score 1.1k · Answer 13 · 2013-10-02 15:28:21

1.1k

Views

Any counter-example to Weierstrass-Stone Thm on non-compact spaces

Published on 02 Oct 2013 - 15:28

score 40 · Answer 14 · 2021-01-26 09:02:06

40

Views

Step 1 in proof of denseness of $\Bbb Q$

Published on 26 Jan 2021 - 9:02

score 186 · Answer 15 · 2022-07-13 15:26:24

186

Views

Is the quotient space of a vector space with a dense subspace isomorphic to the underlying field?

Published on 13 Jul 2022 - 15:26

List Question

Given $\varepsilon > 0$ and an irrational $\alpha$, there exists a rational number $m / n$ that is ($\varepsilon / n$)-close to $\alpha$?

If two function agree on a dense set, what condition is necessary for them to be equal?

The complement of any set of first category on the line is dense iff the intersection of any sequence of dense open sets is dense

Necessity of Hausdorff-ness in "continuous function determined by its values on a dense subset"

A separable normed space that is continuously embedded in a non-separable normed space implies that this embedding isn't dense.

Real Polynomials on Compact sets of Complex numbers

Let $X$ be a normed linear space and let $V \subseteq X$ be a closed linear subspace such that $V \neq X$. Prove that $V$ is nowhere dense.

What is the importance of the density of $C_c^\infty(\mathbb R^n)$ and $L_c^\infty(\mathbb R^n)$ on $L^p(\mathbb R^n)$, for every $1 \leq p < \infty$?

Density argument in Normed spaces

Square integrable for universal approximation

Demonstrating Density Using the Stone-Weierstrass Theorem

Random functions and neuronal network

Any counter-example to Weierstrass-Stone Thm on non-compact spaces

Step 1 in proof of denseness of $\Bbb Q$

Is the quotient space of a vector space with a dense subspace isomorphic to the underlying field?

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