Question

Real line $\mathbb R^1$ with the countable complement topology is not compact

score 1.2k · Answer 1 · 2026-04-12 23:56:04

1.2k

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Real line $\mathbb R^1$ with the countable complement topology is not compact

Published on 12 Apr 2026 - 23:56

score 177 · Answer 2 · 2026-04-15 07:20:48

177

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Show $\mathbb{S}^{2}/\mathbb{S}^{0}$ is homotopy equivalent to $\mathbb{S}^{2} \vee \mathbb{S}^{1}$.

Published on 15 Apr 2026 - 7:20

score 67 · Answer 3 · 2026-04-16 08:49:22

67

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Joint Measurability from Weak Measurability and Continuity

Published on 16 Apr 2026 - 8:49

score 49 · Answer 4 · 2026-04-15 09:53:05

49

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What are the closed sets of this topology.

Published on 15 Apr 2026 - 9:53

score 97 · Answer 5 · 2026-04-16 07:37:05

True or False:Let $X$ be a topological space such that any two nonempty openset in $X$ intersect, then $X$ is compact.

score 77 · Answer 6 · 2026-04-15 20:11:13

77

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If i have two closed and disjoint sets A and B in a set X c $R^{m}$, are there any open and disjoint sets in X that contain A and B?

Published on 15 Apr 2026 - 20:11

score 36 · Answer 7 · 2026-04-12 07:45:42

36

Views

Using ∞-BinFractions to define a topological space homeomorphic to the positive real numbers?

Published on 12 Apr 2026 - 7:45

score 204 · Answer 8 · 2026-04-10 21:16:05

204

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Preimage of continuous function of nonzero measure

Published on 10 Apr 2026 - 21:16

score 108 · Answer 9 · 2026-04-13 17:42:24

108

Views

Continuous maps between $\mathbb N\cup \{\infty\}$ and $\mathbb R$

Published on 13 Apr 2026 - 17:42

score 181 · Answer 10 · 2026-04-11 16:45:20

181

Views

The covering transformation is determined by its value at the base point

Published on 11 Apr 2026 - 16:45

score 104 · Answer 11 · 2026-04-09 03:42:14

104

Views

Is every retraction a bounded map?

Published on 09 Apr 2026 - 3:42

score 40 · Answer 12 · 2026-04-12 05:49:29

40

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Locally compactness

Published on 12 Apr 2026 - 5:49

score 418 · Answer 13 · 2026-04-17 09:18:48

$\{ x : x,c \in \mathbb{R} \land c>0 \land \forall j,k \in \mathbb{Z} \ ( k \ge 0 \Rightarrow |x-j2^{-k}| \ge c2^{-k} ) \}$ dense in $\mathbb{R}$?

score 73 · Answer 14 · 2026-04-11 08:00:47

73

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Prescribed set of continuous functions

Published on 11 Apr 2026 - 8:00

score 134 · Answer 15 · 2026-04-15 14:14:49

Give an example of subset $B$ of the real line $\mathbb{R}$ so the subsets $A$, $Int(A)$, $\overline{A}$, dont intersect

List Question

Real line $\mathbb R^1$ with the countable complement topology is not compact

Show $\mathbb{S}^{2}/\mathbb{S}^{0}$ is homotopy equivalent to $\mathbb{S}^{2} \vee \mathbb{S}^{1}$.

Joint Measurability from Weak Measurability and Continuity

What are the closed sets of this topology.

True or False:Let $X$ be a topological space such that any two nonempty openset in $X$ intersect, then $X$ is compact.

If i have two closed and disjoint sets A and B in a set X c $R^{m}$, are there any open and disjoint sets in X that contain A and B?

Using ∞-BinFractions to define a topological space homeomorphic to the positive real numbers?

Preimage of continuous function of nonzero measure

Continuous maps between $\mathbb N\cup \{\infty\}$ and $\mathbb R$

The covering transformation is determined by its value at the base point

Is every retraction a bounded map?

Locally compactness

$\{ x : x,c \in \mathbb{R} \land c>0 \land \forall j,k \in \mathbb{Z} \ ( k \ge 0 \Rightarrow |x-j2^{-k}| \ge c2^{-k} ) \}$ dense in $\mathbb{R}$?

Prescribed set of continuous functions

Give an example of subset $B$ of the real line $\mathbb{R}$ so the subsets $A$, $Int(A)$, $\overline{A}$, dont intersect

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