List questions from connectedness

Published on 15 Sep 2019 - 20:52

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Check if $(S,d)$ is a connected metric space

Published on 16 Sep 2019 - 12:05

385

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Prove that $A\cup B$ is connected.

Published on 16 Sep 2019 - 21:19

195

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connectedness necessary for the existence of primitive

Published on 19 Sep 2019 - 8:34

47

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Sufficient condition for the union of connected sets to be also connected

Published on 19 Sep 2019 - 14:54

271

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Doubly connected Lorentz group?

Published on 23 Sep 2019 - 2:53

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Every n-manifold is a disjoint union of countably many connected n-manifolds.

Published on 23 Sep 2019 - 10:47

462

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Show that each connected component of $[0,1]-S$ is an open interval $(a,b)$ with $a,b \in S$

Published on 25 Sep 2019 - 13:25

42

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Applications of Graph Theory

Published on 25 Mar 2026 - 11:10

177

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on a connected normal space, applying Urysohn's lemma to show that $f^{-1}(r)$ has nonempty interior for each $r \in \mathbb{Q}\cap I$

Published on 25 Sep 2019 - 22:58

137

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If two spaces $X$ and $Y$ are homotopy equivalent, then $X$ is totally disconnected iff $Y$ is totally disconnected

Published on 26 Sep 2019 - 11:47

102

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How to verify if a specific subset of the simplex is simply connected

Published on 26 Mar 2026 - 6:21

94

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Let $f:S^1 \rightarrow \mathbb{R}$ be a continous function. Show that exists $x\in S^1$ such that $f(x)=f(-x)$

Published on 29 Sep 2019 - 20:29

116

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Does connectedness of $cl(A)$ implies $A$ is connected?

Published on 01 Oct 2019 - 15:36

38

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Product of nonzero ideals in a connected ring

Published on 01 Oct 2019 - 21:06

List Question

Prove that each connected component is closed

Check if $(S,d)$ is a connected metric space

Prove that $A\cup B$ is connected.

connectedness necessary for the existence of primitive

Sufficient condition for the union of connected sets to be also connected

Doubly connected Lorentz group?

Every n-manifold is a disjoint union of countably many connected n-manifolds.

Show that each connected component of $[0,1]-S$ is an open interval $(a,b)$ with $a,b \in S$

Applications of Graph Theory

on a connected normal space, applying Urysohn's lemma to show that $f^{-1}(r)$ has nonempty interior for each $r \in \mathbb{Q}\cap I$

If two spaces $X$ and $Y$ are homotopy equivalent, then $X$ is totally disconnected iff $Y$ is totally disconnected

How to verify if a specific subset of the simplex is simply connected

Let $f:S^1 \rightarrow \mathbb{R}$ be a continous function. Show that exists $x\in S^1$ such that $f(x)=f(-x)$

Does connectedness of $cl(A)$ implies $A$ is connected?

Product of nonzero ideals in a connected ring

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