Question

Proving existence of sequence of finite, clopen and disjoint cover each member with diameter at most $1/n.$

score 56 · Answer 1 · 2020-04-10 11:14:24

56

Views

Proving existence of sequence of finite, clopen and disjoint cover each member with diameter at most $1/n.$

Published on 10 Apr 2020 - 11:14

score 71 · Answer 2 · 2020-04-10 23:11:01

71

Views

Show that $\mathcal{A}$ is a basis for the topology on $X.$

Published on 10 Apr 2020 - 23:11

score 130 · Answer 3 · 2020-04-10 23:40:19

130

Views

Rudin RCA Theorem 2.7: Why do we need $G$?

Published on 10 Apr 2020 - 23:40

score 42 · Answer 4 · 2020-04-11 14:09:29

42

Views

Investigating the relationship between $X$ and the inverse limit $\mathcal{L}$ of the tower.

Published on 11 Apr 2020 - 14:09

score 38 · Answer 5 · 2020-04-11 15:15:19

38

Views

Find a way to uniquely determine a point $x_{\sigma} \in X,$ given an element $\sigma \in \mathcal{L}$

Published on 11 Apr 2020 - 15:15

score 151 · Answer 6 · 2020-04-11 17:56:52

151

Views

If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.

Published on 11 Apr 2020 - 17:56

score 51 · Answer 7 · 2020-04-11 22:54:16

51

Views

Showing that $X$ and the inverse limit of the sequence $\mathcal{L}$ are homeomorphic.

Published on 11 Apr 2020 - 22:54

score 42 · Answer 8 · 2020-04-12 10:45:25

42

Views

Is $\mathbb{N}$ a totally bounded metric space with this metric $d(a,b) = \sqrt{1-2\frac{\gcd(a,b)}{a+b}}$?

Published on 12 Apr 2020 - 10:45

score 403 · Answer 9 · 2020-04-12 23:08:24

403

Views

Prove that if Y is a closed and bounded subset of $R^{N}$ then Y is complete and totally bounded (pre-compact).

Published on 12 Apr 2020 - 23:08

score 93 · Answer 10 · 2020-04-14 07:13:38

93

Views

Show by an example that a proper closed subset of $\mathbb{R}$ in the sandard (order) topology need not be compact.

Published on 14 Apr 2020 - 7:13

score 32 · Answer 11 · 2020-04-15 07:41:12

32

Views

A metric space in which every point is contained in a ball whose closure is compact.

Published on 15 Apr 2020 - 7:41

score 62 · Answer 12 · 2020-04-15 13:13:42

62

Views

Help! I can't think why it has to be closed as well.

Published on 15 Apr 2020 - 13:13

score 176 · Answer 13 · 2020-04-15 23:29:02

176

Views

Let $A \subset \mathbb{R}$ and $B \subset \mathbb{R}$ be two compact sets. Prove that $A/B, e^A$ and $e^A + e^B$ are compact sets

Published on 15 Apr 2020 - 23:29

score 44 · Answer 14 · 2020-04-16 13:43:17

44

Views

prove that the set A/B is compact

Published on 16 Apr 2020 - 13:43

score 40 · Answer 15 · 2020-04-16 21:24:58

40

Views

Partitioning the Domain of a Curve

Published on 16 Apr 2020 - 21:24

List Question

Proving existence of sequence of finite, clopen and disjoint cover each member with diameter at most $1/n.$

Show that $\mathcal{A}$ is a basis for the topology on $X.$

Rudin RCA Theorem 2.7: Why do we need $G$?

Investigating the relationship between $X$ and the inverse limit $\mathcal{L}$ of the tower.

Find a way to uniquely determine a point $x_{\sigma} \in X,$ given an element $\sigma \in \mathcal{L}$

If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.

Showing that $X$ and the inverse limit of the sequence $\mathcal{L}$ are homeomorphic.

Is $\mathbb{N}$ a totally bounded metric space with this metric $d(a,b) = \sqrt{1-2\frac{\gcd(a,b)}{a+b}}$?

Prove that if Y is a closed and bounded subset of $R^{N}$ then Y is complete and totally bounded (pre-compact).

Show by an example that a proper closed subset of $\mathbb{R}$ in the sandard (order) topology need not be compact.

A metric space in which every point is contained in a ball whose closure is compact.

Help! I can't think why it has to be closed as well.

Let $A \subset \mathbb{R}$ and $B \subset \mathbb{R}$ be two compact sets. Prove that $A/B, e^A$ and $e^A + e^B$ are compact sets

prove that the set A/B is compact

Partitioning the Domain of a Curve

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