Skip to main content
MathOverflow

Return to Answer

Minor Math Jaxing (bracket scaling)
Source Link
Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45

It seems if you take $B=\mathbb{R}^2$ and $B'$ the complement of the closure of $\{(x,\sin(\frac{1}{x}));x\in(0,\infty)\}$$\Big\{\big(x,\sin\big(\frac{1}{x}\big)\big);x\in(0,\infty)\Big\}$ this is a counterexample. (Added bonus: $B'$ is also simply connected)

It seems if you take $B=\mathbb{R}^2$ and $B'$ the complement of the closure of $\{(x,\sin(\frac{1}{x}));x\in(0,\infty)\}$ this is a counterexample. (Added bonus: $B'$ is also simply connected)

It seems if you take $B=\mathbb{R}^2$ and $B'$ the complement of the closure of $\Big\{\big(x,\sin\big(\frac{1}{x}\big)\big);x\in(0,\infty)\Big\}$ this is a counterexample. (Added bonus: $B'$ is also simply connected)

Source Link
Saúl RM
Saúl RM
  • 10.6k
  • 2
  • 28
  • 48

It seems if you take $B=\mathbb{R}^2$ and $B'$ the complement of the closure of $\{(x,\sin(\frac{1}{x}));x\in(0,\infty)\}$ this is a counterexample. (Added bonus: $B'$ is also simply connected)