Question

Is the weak$^*$ topology the same as the inherited product topology?

score 429 · Answer 1 · 2018-05-01 10:27:48

429

Views

Is the weak$^*$ topology the same as the inherited product topology?

Published on 01 May 2018 - 10:27

score 45 · Answer 2 · 2026-03-28 02:42:56

45

Views

Let A be a nonempty open subset of $\mathbb{C}$. Then is it possible that $A \cup {u}$ for any $u$ $\in$ $\mathbb{C}$

Published on 28 Mar 2026 - 2:42

score 80 · Answer 3 · 2018-05-01 10:44:49

80

Views

Check if this set is compact: $\{ (x,y,z) \in \mathbb R^3 \mid |x| \le 1 \land y = 0 \land 0 \le z \le |x| \}$

Published on 01 May 2018 - 10:44

score 256 · Answer 4 · 2026-03-28 08:49:09

256

Views

Proof of Banach Alaoglu without nets

Published on 28 Mar 2026 - 8:49

score 89 · Answer 5 · 2026-03-25 23:13:04

89

Views

If $(X, d_x)$ and $(Y, d_Y)$ are connected show that $(X \times Y, d)$ where $d((x_1, y_1), (x_2, y_2)) = d_x(x_1, x_2) + d_Y(y_1, y_2)$ is connected

Published on 25 Mar 2026 - 23:13

score 86 · Answer 6 · 2026-03-29 23:55:58

86

Views

Properties of the closure in $\{0,1\}^\mathbb N$ of all shifts of a word

Published on 29 Mar 2026 - 23:55

score 843 · Answer 7 · 2026-03-25 07:54:28

843

Views

How can we check if the set is path-connected?

Published on 25 Mar 2026 - 7:54

score 1k · Answer 8 · 2026-03-29 23:45:20

1k

Views

Equivalence of continuity between metric and topological spaces

Published on 29 Mar 2026 - 23:45

score 1.1k · Answer 9 · 2026-03-25 17:37:45

1.1k

Views

Properties of inclusion map between topological spaces.

Published on 25 Mar 2026 - 17:37

score 133 · Answer 10 · 2026-04-01 20:23:47

133

Views

Topology Proof Advice/Guidance

Published on 01 Apr 2026 - 20:23

score 70 · Answer 11 · 2026-03-25 01:23:53

70

Views

Is $\prod_{i \in I} f_i$ continuous?

Published on 25 Mar 2026 - 1:23

score 217 · Answer 12 · 2026-03-30 08:54:18

217

Views

Proving the Kernel is a free group

Published on 30 Mar 2026 - 8:54

score 54 · Answer 13 · 2018-05-01 22:42:41

54

Views

How do I prove a subspace is discrete?

Published on 01 May 2018 - 22:42

score 1.1k · Answer 14 · 2026-03-29 13:23:22

1.1k

Views

Preservation of closed sets under linear transformation.

Published on 29 Mar 2026 - 13:23

score 129 · Answer 15 · 2026-04-01 09:02:02

129

Views

General conditions for the Fixed point property on the Quotient topology

Published on 01 Apr 2026 - 9:02

List Question

Is the weak$^*$ topology the same as the inherited product topology?

Let A be a nonempty open subset of $\mathbb{C}$. Then is it possible that $A \cup {u}$ for any $u$ $\in$ $\mathbb{C}$

Check if this set is compact: $\{ (x,y,z) \in \mathbb R^3 \mid |x| \le 1 \land y = 0 \land 0 \le z \le |x| \}$

Proof of Banach Alaoglu without nets

If $(X, d_x)$ and $(Y, d_Y)$ are connected show that $(X \times Y, d)$ where $d((x_1, y_1), (x_2, y_2)) = d_x(x_1, x_2) + d_Y(y_1, y_2)$ is connected

Properties of the closure in $\{0,1\}^\mathbb N$ of all shifts of a word

How can we check if the set is path-connected?

Equivalence of continuity between metric and topological spaces

Properties of inclusion map between topological spaces.

Topology Proof Advice/Guidance

Is $\prod_{i \in I} f_i$ continuous?

Proving the Kernel is a free group

How do I prove a subspace is discrete?

Preservation of closed sets under linear transformation.

General conditions for the Fixed point property on the Quotient topology

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