Closed Set

analysis

Definition

Closed Set

A closed set is a generalisation of a closed interval.

Let $S$ be a set:

$$S\text{is closed}⟺\exists (s_n{)}_{n\in \mathbb{N}}\in S^{\mathbb{N}}:\underset{n\to \infty }{\lim }{s}_n\in S$$

The limit of an arbitrary sequence built from $S$ is again element of $S$.