Question

What is the difference between a dense set and an $\varepsilon$-dense set?

score 83 · Answer 1 · 2018-04-16 23:46:26

83

Views

What is the difference between a dense set and an $\varepsilon$-dense set?

Published on 16 Apr 2018 - 23:46

score 27 · Answer 2 · 2018-04-17 01:53:38

27

Views

How is it possible that there is no such $n$ that would make $A$ isolated?

Published on 17 Apr 2018 - 1:53

score 388 · Answer 3 · 2018-04-17 14:06:10

388

Views

Proof Review for Triangle Inequality for $d((x_1, x_2), (y_1, y_2)) = max( |y_1 - x_1|, |y_2 - x_2|)$

Published on 17 Apr 2018 - 14:06

score 22 · Answer 4 · 2018-04-17 19:27:51

Let $(X, d)$be a metric space and suppose that $Y \subseteq X$ is bounded by $B(x, r)$, what is the smallest $r'$ s.t $\bar{Y} \subseteq B(x, r')$

score 43 · Answer 5 · 2026-03-29 16:39:55

43

Views

Showing continuity of $\operatorname{Id} : (C^0([0,1], L^\infty) \to (C^0([0,1], L^1)$, proof question

Published on 29 Mar 2026 - 16:39

score 421 · Answer 6 · 2026-03-20 06:42:54

421

Views

Show that free group $\mathbb{F}_2$ is not amenable using Hulanicki-Reiter condition.

Published on 20 Mar 2026 - 6:42

score 1.6k · Answer 7 · 2026-03-25 16:54:17

1.6k

Views

Relationship between equicontinuity and total boundedness

Published on 25 Mar 2026 - 16:54

score 157 · Answer 8 · 2026-03-25 10:56:07

157

Views

For which subsets of $\mathbb{R}$ do the metric completion and the order completion coincide?

Published on 25 Mar 2026 - 10:56

score 74 · Answer 9 · 2018-04-20 02:57:16

74

Views

Regarding the definition of totally bounded spaces

Published on 20 Apr 2018 - 2:57

score 1k · Answer 10 · 2026-03-24 22:01:49

1k

Views

Preparation for Folland/Royden/Graduate-Level Analysis

Published on 24 Mar 2026 - 22:01

score 266 · Answer 11 · 2026-03-29 18:13:35

266

Views

Triangle Inequality Proof Review for $d(x, y) = |x^2 - y^2|$

Published on 29 Mar 2026 - 18:13

score 1.3k · Answer 12 · 2026-03-25 04:40:12

1.3k

Views

Uniformly continuous functions and the preservation of Cauchy sequences

Published on 25 Mar 2026 - 4:40

score 144 · Answer 13 · 2018-04-20 20:13:59

144

Views

Only the empty set is equal to the interior of its boundary.

Published on 20 Apr 2018 - 20:13

score 615 · Answer 14 · 2018-04-21 04:54:47

615

Views

Proof of topological equivalence

Published on 21 Apr 2018 - 4:54

score 120 · Answer 15 · 2026-03-25 21:22:16

120

Views

Show that the X is disconnected

Published on 25 Mar 2026 - 21:22

List Question

What is the difference between a dense set and an $\varepsilon$-dense set?

How is it possible that there is no such $n$ that would make $A$ isolated?

Proof Review for Triangle Inequality for $d((x_1, x_2), (y_1, y_2)) = max( |y_1 - x_1|, |y_2 - x_2|)$

Let $(X, d)$be a metric space and suppose that $Y \subseteq X$ is bounded by $B(x, r)$, what is the smallest $r'$ s.t $\bar{Y} \subseteq B(x, r')$

Showing continuity of $\operatorname{Id} : (C^0([0,1], L^\infty) \to (C^0([0,1], L^1)$, proof question

Show that free group $\mathbb{F}_2$ is not amenable using Hulanicki-Reiter condition.

Relationship between equicontinuity and total boundedness

For which subsets of $\mathbb{R}$ do the metric completion and the order completion coincide?

Regarding the definition of totally bounded spaces

Preparation for Folland/Royden/Graduate-Level Analysis

Triangle Inequality Proof Review for $d(x, y) = |x^2 - y^2|$

Uniformly continuous functions and the preservation of Cauchy sequences

Only the empty set is equal to the interior of its boundary.

Proof of topological equivalence

Show that the X is disconnected

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