eng

### open set <metric, topology, geometry>

containing a metric or topologically open neighborhood of each of its points

Note to entry: In a metric space, a set `X` us open if each point `x` in the set is contained in some small ball which is a subset of \(X:\) \([X \text{ is open}] \Leftrightarrow [x \in X] \implies [\exists \varepsilon > 0 \backepsilon \text{distance} (x,y) < \varepsilon] \implies [y \in X]\). A topology is a set of subsets of a space which are considered open.

ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)