- #1

Rasalhague

- 1,387

- 2

[tex]\overline{A}\setminus\overline{B} \subseteq \overline{A\setminus B}.[/tex]

Now [itex]x\in\overline{A}\setminus\overline{B}[/itex] means x is in every closed superset of A but there exists a closed superset of B that doesn't contain x, whereas [itex]x\in \overline{A\setminus B}[/itex] means x is in every closed set that contains every point of A that's not also in B.

I've tried various manipulations involving equivalent definitions of closure, but have yet to find any obvious way to proceed. Any hints?