Question

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

score 53 · Answer 1 · 2026-05-05 07:47:32

53

Views

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

Published on 05 May 2026 - 7:47

score 77 · Answer 2 · 2026-05-05 11:52:37

77

Views

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

Published on 05 May 2026 - 11:52

score 70 · Answer 3 · 2026-05-05 10:04:44

70

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 05 May 2026 - 10:04

score 90 · Answer 4 · 2026-05-05 00:50:23

90

Views

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

Published on 05 May 2026 - 0:50

score 35 · Answer 5 · 2026-05-05 04:20:10

35

Views

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

Published on 05 May 2026 - 4:20

score 84 · Answer 6 · 2026-05-05 09:00:29

84

Views

Real Polynomials on Compact sets of Complex numbers

Published on 05 May 2026 - 9:00

score 35 · Answer 7 · 2026-05-05 05:27:09

35

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 05 May 2026 - 5:27

score 70 · Answer 8 · 2026-05-05 04:20:29

70

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 05 May 2026 - 4:20

score 58 · Answer 9 · 2026-05-05 08:15:43

58

Views

Density argument in Normed spaces

Published on 05 May 2026 - 8:15

score 113 · Answer 10 · 2026-05-05 06:46:25

113

Views

Square integrable for universal approximation

Published on 05 May 2026 - 6:46

score 118 · Answer 11 · 2026-05-05 10:13:01

118

Views

Demonstrating Density Using the Stone-Weierstrass Theorem

Published on 05 May 2026 - 10:13

score 17 · Answer 12 · 2026-05-05 12:52:02

17

Views

Random functions and neuronal network

Published on 05 May 2026 - 12:52

score 1.1k · Answer 13 · 2026-05-05 01:55:37

1.1k

Views

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

Published on 05 May 2026 - 1:55

score 44 · Answer 14 · 2026-05-04 22:41:28

44

Views

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

Published on 04 May 2026 - 22:41

score 190 · Answer 15 · 2026-05-05 01:17:45

190

Views

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

Published on 05 May 2026 - 1:17

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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