List questions from connectedness

Published on 23 Jun 2014 - 20:16

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is $(\mathbb{Q} \times (\mathbb{R}\setminus\mathbb{Q}))\cup((\mathbb{R}\setminus\mathbb{Q})\times\mathbb{Q})$ connected? path connected?

Published on 30 Mar 2026 - 8:01

127

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Is a topological space determined by its components and their quotient?

Published on 25 Jun 2014 - 10:08

1.6k

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Countable subsets are disconnected

Published on 25 Jun 2014 - 10:55

574

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If $p : E \to B$ is a covering map and $E$ is simply connected, then each fiber of $p$ has the cardinality of that of $\pi_1(B)$.

Published on 26 Mar 2026 - 19:19

177

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Proving a region is pathwise connected

Published on 26 Jun 2014 - 19:02

221

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Prove: If H and G/H are totally disconnected then G is also totally disconnected

Published on 26 Mar 2026 - 11:08

935

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$A\cup B$ is connected when $A$ is connected in $X$ and $B$ clopen in $X-A$

Published on 29 Jun 2014 - 19:58

1.3k

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Good Methods for Proving Connectedness

Published on 30 Jun 2014 - 20:59

343

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When does connectedness imply path-connectedness

Published on 05 Jul 2014 - 18:31

1.6k

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Connected bipartite graph

Published on 25 Mar 2026 - 17:16

69

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Product of Connected Spaces (2)

Published on 07 Jul 2014 - 13:32

662

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Closed and Connected subgroups of $\mathbb{R}^n$

Published on 26 Mar 2026 - 19:06

336

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Homotopy of Involutory Matrices?

Published on 09 Jul 2014 - 12:24

97

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Need help understanding proof about connected sets.

Published on 14 Jul 2014 - 18:36

List Question

Proof: The quotient space is totally disconnected

is $(\mathbb{Q} \times (\mathbb{R}\setminus\mathbb{Q}))\cup((\mathbb{R}\setminus\mathbb{Q})\times\mathbb{Q})$ connected? path connected?

Is a topological space determined by its components and their quotient?

Countable subsets are disconnected

If $p : E \to B$ is a covering map and $E$ is simply connected, then each fiber of $p$ has the cardinality of that of $\pi_1(B)$.

Proving a region is pathwise connected

Prove: If H and G/H are totally disconnected then G is also totally disconnected

$A\cup B$ is connected when $A$ is connected in $X$ and $B$ clopen in $X-A$

Good Methods for Proving Connectedness

When does connectedness imply path-connectedness

Connected bipartite graph

Product of Connected Spaces (2)

Closed and Connected subgroups of $\mathbb{R}^n$

Homotopy of Involutory Matrices?

Need help understanding proof about connected sets.

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