Question

Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

score 23.6k · Answer 1 · 2026-03-31 06:04:46

23.6k

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Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

Published on 31 Mar 2026 - 6:04

score 1.3k · Answer 2 · 2014-10-02 00:10:33

1.3k

Views

What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?

Published on 02 Oct 2014 - 0:10

score 290 · Answer 3 · 2026-03-27 13:38:17

290

Views

$k$-connected graphs containing trees

Published on 27 Mar 2026 - 13:38

score 132 · Answer 4 · 2014-10-04 07:35:57

132

Views

Connectedness and locally path-connectedness

Published on 04 Oct 2014 - 7:35

score 478 · Answer 5 · 2014-10-05 23:27:16

478

Views

Is the one point compactification of the set $\{xy = 0\}\in \mathbb R^2$ minus any point connected?

Published on 05 Oct 2014 - 23:27

score 464 · Answer 6 · 2014-10-06 00:23:59

464

Views

If $E$ and $F$ are nonempty subsets of $M$ and if $E \cup F$ is connected, show that $\bar{E} \cap \bar{F} \neq \emptyset$

Published on 06 Oct 2014 - 0:23

score 563 · Answer 7 · 2026-03-25 22:24:49

563

Views

Planar graphs and connectivity

Published on 25 Mar 2026 - 22:24

score 115 · Answer 8 · 2014-10-08 01:03:26

115

Views

If $ y \in [0,1] \times [0,1]$, is $[0,1] \times [0,1]-y$ connected?

Published on 08 Oct 2014 - 1:03

score 241 · Answer 9 · 2026-03-25 06:01:58

241

Views

(Path)Connectedness of $w^{2} = \sin z$.

Published on 25 Mar 2026 - 6:01

score 74 · Answer 10 · 2014-10-08 09:17:20

74

Views

Proof Verification : If $S$ is a metric space and $U(x)$ is the component of $S$ containing $x$, then is $U(x)$ closed in $S$ .

Published on 08 Oct 2014 - 9:17

score 392 · Answer 11 · 2014-10-11 12:50:16

392

Views

Boundary bumping theorem

Published on 11 Oct 2014 - 12:50

score 215 · Answer 12 · 2014-10-11 18:51:49

215

Views

Is the following subset of a plane connected? (picture)

Published on 11 Oct 2014 - 18:51

score 625 · Answer 13 · 2014-10-12 13:45:47

625

Views

Set $S$ which is path-connected, but $\overline{S}$ is not path-connected

Published on 12 Oct 2014 - 13:45

score 69 · Answer 14 · 2014-10-12 15:40:05

69

Views

is C[a,b] with 1-norm connected

Published on 12 Oct 2014 - 15:40

score 400 · Answer 15 · 2014-10-14 02:01:45

400

Views

What characteristics of binary space are needed to prove that it is totally disconnected?

Published on 14 Oct 2014 - 2:01

List Question

Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?

$k$-connected graphs containing trees

Connectedness and locally path-connectedness

Is the one point compactification of the set $\{xy = 0\}\in \mathbb R^2$ minus any point connected?

If $E$ and $F$ are nonempty subsets of $M$ and if $E \cup F$ is connected, show that $\bar{E} \cap \bar{F} \neq \emptyset$

Planar graphs and connectivity

If $ y \in [0,1] \times [0,1]$, is $[0,1] \times [0,1]-y$ connected?

(Path)Connectedness of $w^{2} = \sin z$.

Proof Verification : If $S$ is a metric space and $U(x)$ is the component of $S$ containing $x$, then is $U(x)$ closed in $S$ .

Boundary bumping theorem

Is the following subset of a plane connected? (picture)

Set $S$ which is path-connected, but $\overline{S}$ is not path-connected

is C[a,b] with 1-norm connected

What characteristics of binary space are needed to prove that it is totally disconnected?

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