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## Homework Statement

## The Attempt at a Solution

I've got through this question up to the last bit.

I've got [itex]B(0,1) = \{0\}[/itex] and [itex]B(0,2) = \{y\in\mathbb{R} : -1<y<1 \}[/itex] (i.e. the open interval (-1,1).)

How do I show that every subset of [itex]\mathbb{R}[/itex] is open ([itex]A \subseteq X[/itex] is open if it contains none if its boundary)

and then find which subsets are closed?