Question

Is $ \left\{\cup _{n \in \mathbb{N} } (x, x^n) \mid x \in [0,1] \right\} $ compact?

score 38 · Answer 1 · 2019-02-05 17:40:54

38

Views

Is $ \left\{\cup _{n \in \mathbb{N} } (x, x^n) \mid x \in [0,1] \right\} $ compact?

Published on 05 Feb 2019 - 17:40

score 67 · Answer 2 · 2026-03-30 01:29:46

67

Views

Non compacity of a subset of $\ell^1$

Published on 30 Mar 2026 - 1:29

score 122 · Answer 3 · 2026-03-25 03:21:15

122

Views

Theorem 3.20 rudin's functional analysis, compactness of $K = f(S \times A)$

Published on 25 Mar 2026 - 3:21

score 90 · Answer 4 · 2019-02-07 01:42:27

90

Views

Proof Clarification: Show that every sequence of a compact set $S \subset \mathbb{R}$ has a subsequence which converges in $S$.

Published on 07 Feb 2019 - 1:42

score 61 · Answer 5 · 2019-02-10 08:22:47

61

Views

How do I know $x \in \bigcap\limits_{n = 1}^\infty f^{-1}([n,\infty))$?

Published on 10 Feb 2019 - 8:22

score 63 · Answer 6 · 2026-03-29 16:21:28

63

Views

Compact or open $\{0\}\cup\{\frac1n + \frac1m | m,n \in N\})$ in R?

Published on 29 Mar 2026 - 16:21

score 57 · Answer 7 · 2019-02-12 05:47:05

57

Views

Given $E \subset \mathbb{R^n}$ with $m^(E) < \infty$. Show that if $E$ is compact then $m^(E) = \lim_{m \to \infty} m^*(\sigma_m)$

Published on 12 Feb 2019 - 5:47

score 4.2k · Answer 8 · 2019-02-12 18:38:27

4.2k

Views

Why are subsets of compact sets not compact?

Published on 12 Feb 2019 - 18:38

score 2.4k · Answer 9 · 2019-02-13 01:01:10

2.4k

Views

Proving that a subset of $l^{2}$ is compact

Published on 13 Feb 2019 - 1:01

score 450 · Answer 10 · 2026-03-25 11:04:49

450

Views

Are neural networks with bounded parameters a compact subset of the Banach space of continuous functions?

Published on 25 Mar 2026 - 11:04

score 274 · Answer 11 · 2026-03-27 06:15:06

274

Views

Metric spaces problem regarding if composition function is uniformly continuous then what about individual function itself

Published on 27 Mar 2026 - 6:15

score 150 · Answer 12 · 2026-03-27 21:20:30

150

Views

Show that $K∩L$ is homeomorphic to $A$, where $K ∩ L = \{\{(a,0),(a,1)\} : a \in A\}$ is a subset of equivalence classes in $[0,1] \times \{0,1\}$.

Published on 27 Mar 2026 - 21:20

score 4.4k · Answer 13 · 2026-03-30 01:28:39

4.4k

Views

Show that $\mathbb{R^{n}}$ is not compact by definition

Published on 30 Mar 2026 - 1:28

score 226 · Answer 14 · 2019-02-18 21:17:45

226

Views

Theorem 2.34 Baby Rudin (Compact subsets of metric spaces are closed): How is his proof general enough?

Published on 18 Feb 2019 - 21:17

score 134 · Answer 15 · 2026-03-26 10:56:19

134

Views

Rudin Functional Analysis Theorem 3.25

Published on 26 Mar 2026 - 10:56

List Question

Is $ \left\{\cup _{n \in \mathbb{N} } (x, x^n) \mid x \in [0,1] \right\} $ compact?

Non compacity of a subset of $\ell^1$

Theorem 3.20 rudin's functional analysis, compactness of $K = f(S \times A)$

Proof Clarification: Show that every sequence of a compact set $S \subset \mathbb{R}$ has a subsequence which converges in $S$.

How do I know $x \in \bigcap\limits_{n = 1}^\infty f^{-1}([n,\infty))$?

Compact or open $\{0\}\cup\{\frac1n + \frac1m | m,n \in N\})$ in R?

Given $E \subset \mathbb{R^n}$ with $m^(E) < \infty$. Show that if $E$ is compact then $m^(E) = \lim_{m \to \infty} m^*(\sigma_m)$

Why are subsets of compact sets not compact?

Proving that a subset of $l^{2}$ is compact

Are neural networks with bounded parameters a compact subset of the Banach space of continuous functions?

Metric spaces problem regarding if composition function is uniformly continuous then what about individual function itself

Show that $K∩L$ is homeomorphic to $A$, where $K ∩ L = \{\{(a,0),(a,1)\} : a \in A\}$ is a subset of equivalence classes in $[0,1] \times \{0,1\}$.

Show that $\mathbb{R^{n}}$ is not compact by definition

Theorem 2.34 Baby Rudin (Compact subsets of metric spaces are closed): How is his proof general enough?

Rudin Functional Analysis Theorem 3.25

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