2
votes
4answers
202 views

$\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ open or closed [duplicate]

Possible Duplicate: Proving that a complex set in open/closed/neither and bounded/not bounded I think $\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ is closed. But I have ...
0
votes
2answers
215 views

Limit Points within a Set

If I have an uncountable subset $A \in \mathbb{R}$, and we assume A is nonempty, does it follow that every point within $A$ is a limit point of $A$ from the density of $\mathbb{Q}$ in $\mathbb{R}$ ...