Suppose that $X$ is a metric space with a nowhere dense subset $A$. Say that $x$ is a point in $X \setminus A$.
Then it must be the case that there exists an $r>0$ such that $B(x,r) \cap A = \varnothing$?
Any hint would be appreciated.
Asked
Active
Viewed 29 times
0
-
3What if $X=\mathbb R$ and $A={\frac1n:n\in\mathbb N}$ and $x=0?$ – bof Apr 21 '17 at 04:33
-
1Your statement is true if you change "nowhere dense" to "closed". – bof Apr 21 '17 at 04:34