I need to find an example of a closed set $E$ that is not an interval and not compact and a bounded set $F$ that is not an interval and not compact.
I'm really confused how to find this without using an interval
2026-04-19 02:00:16.1776564016
finding noninterval sets that are either closed and unbounded or bounded and open
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Give $\mathbb{R}$ the discrete topology. Then $\mathbb{N}$ is closed (every set is closed in the discrete topology) in $\mathbb{R}$. But it is not compact nor is it an interval.
For the second part, give $\mathbb{R}$ its usual topology. Let $F = (0,1) \cup \{2\}$. It is not an interval, it is bounded, and it is not compact.