ISO TC 211 Geographic information/Geomatics

# ISO/TC 211 Geolexica

## Concept “open set <metric, topology, geometry>”

Term ID

2245

source

ISO 19107:2019, (E), 3.73

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)

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info

• status: valid
• classification: preferred
• date accepted: 2019-12-02

Review

last review performed:
(2019-12-02)
status:
final
decision:
accepted
decision event:
Normal ISO processing
notes:
Publication of document ISO 19107:2019(E)