ISO TC 211 Geographic information/Geomatics

# ISO/TC 211 Geolexica

## Concept “homomorphism <mathematics>”

Term ID

2168

source

ISO 19107:2019, (E), 3.59

eng

### homomorphism <mathematics>

relationship between two domains such that there is a structure-preserving function from one to the other

Note to entry: A homomorphism is distinct from a isomorphism in that no inverse function is required. In an isomorphism, there are two homomorphisms that are functional inverses of one another. Continuous functions are topological homomorphisms because they preserve "topological characteristics". The mapping of topological complexes to their geometric realizations preserves the concept of boundary and is therefore a homomorphism.

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:
Publication of document ISO 19107:2019(E)
notes:
This entry supersedes the entry for homomorphism in ISO 19107:2003(E)