If G is an open subset of a metric space, is it true that $\text{int}(\bar{G}) = G$?

Question

I have not been able to find a counter example or a proof. Any hints?

Look at $G=(0,1)\cup(1,2)$ in $\Bbb R$. – Brian M. Scott Mar 19 '16 at 18:33 — Brian M. Scott, Mar 19 '16 at 18:33

score 2 · Accepted Answer · answered Mar 19 '16 at 18:35

2

Consider $X=(a,b)\cup (b,c)\subset \mathbb{R}$. $\overline{X}=[a,c],$ and $int(\overline{X})=(a,c)\ne (a,b)\cup (b,c).$

answered Mar 19 '16 at 18:35

Alekos Robotis

1 Answers1