Question

Let $P = \{(x,y) \in \mathbb R^2 : x^2+y^2<1 \}$ and $Q = \{(1,x) : x \in \mathbb R\}$. Is $X=P \cup Q$ connected?

score 111 · Answer 1 · 2018-04-06 20:07:01

111

Views

Let $P = \{(x,y) \in \mathbb R^2 : x^2+y^2<1 \}$ and $Q = \{(1,x) : x \in \mathbb R\}$. Is $X=P \cup Q$ connected?

Published on 06 Apr 2018 - 20:07

score 111 · Answer 2 · 2018-04-07 18:52:43

111

Views

Why is $\operatorname{Bd}(A) = \{0, 1\}$ not connected and $\operatorname{int}(\Bbb Q) = \varnothing$ connected?

Published on 07 Apr 2018 - 18:52

score 884 · Answer 3 · 2018-04-09 03:07:08

884

Views

Union of two compact totally disconnected sets in $\mathbb{R}$ is totally disconnected

Published on 09 Apr 2018 - 3:07

score 60 · Answer 4 · 2026-03-25 07:51:12

60

Views

Munkre topology Section 25 question 1

Published on 25 Mar 2026 - 7:51

score 27 · Answer 5 · 2018-04-11 21:16:54

27

Views

Is $\bigcup \bar{A_i}$ contained, strictly contained, equal or not contained in $C$?

Published on 11 Apr 2018 - 21:16

score 164 · Answer 6 · 2018-04-12 17:49:22

164

Views

Showing $\{ 0, 1 \}^{\mathbb{N}} $ is totally disconnected with given metric

Published on 12 Apr 2018 - 17:49

score 159 · Answer 7 · 2026-03-22 09:51:05

159

Views

Connected components of an open subset

Published on 22 Mar 2026 - 9:51

score 153 · Answer 8 · 2018-04-14 20:22:24

153

Views

A counterexample to the Sura-Bura Theorem for non separated compact spaces

Published on 14 Apr 2018 - 20:22

score 588 · Answer 9 · 2026-03-22 20:13:46

588

Views

Can a countable dense subset be split into two disjoint dense subsets?

Published on 22 Mar 2026 - 20:13

score 33 · Answer 10 · 2026-03-25 06:05:55

33

Views

Connectedness, Products of Finite Topologies

Published on 25 Mar 2026 - 6:05

score 761 · Answer 11 · 2026-03-25 07:58:39

761

Views

Question about link between Julia set and Mandelbrot Set

Published on 25 Mar 2026 - 7:58

score 44 · Answer 12 · 2018-04-16 15:38:47

44

Views

Connectedness of $\mathbb{C} \setminus E$ given $E$ is connected.

Published on 16 Apr 2018 - 15:38

score 40 · Answer 13 · 2018-04-16 22:47:41

40

Views

Conjecture on connectedness using cartesian equation

Published on 16 Apr 2018 - 22:47

score 46 · Answer 14 · 2018-04-17 14:00:30

46

Views

Connected subsets of $\mathbb{R}^2$

Published on 17 Apr 2018 - 14:00

score 203 · Answer 15 · 2018-04-17 20:55:11

203

Views

If $x \in \operatorname{cl}(A)$, where $A$ is a connected subspace of a topological space $X$, then $A \cup \{x\}$ is connected.

Published on 17 Apr 2018 - 20:55

List Question

Let $P = \{(x,y) \in \mathbb R^2 : x^2+y^2<1 \}$ and $Q = \{(1,x) : x \in \mathbb R\}$. Is $X=P \cup Q$ connected?

Why is $\operatorname{Bd}(A) = \{0, 1\}$ not connected and $\operatorname{int}(\Bbb Q) = \varnothing$ connected?

Union of two compact totally disconnected sets in $\mathbb{R}$ is totally disconnected

Munkre topology Section 25 question 1

Is $\bigcup \bar{A_i}$ contained, strictly contained, equal or not contained in $C$?

Showing $\{ 0, 1 \}^{\mathbb{N}} $ is totally disconnected with given metric

Connected components of an open subset

A counterexample to the Sura-Bura Theorem for non separated compact spaces

Can a countable dense subset be split into two disjoint dense subsets?

Connectedness, Products of Finite Topologies

Question about link between Julia set and Mandelbrot Set

Connectedness of $\mathbb{C} \setminus E$ given $E$ is connected.

Conjecture on connectedness using cartesian equation

Connected subsets of $\mathbb{R}^2$

If $x \in \operatorname{cl}(A)$, where $A$ is a connected subspace of a topological space $X$, then $A \cup \{x\}$ is connected.

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