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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Topological group

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Summary

A group whose operations are continuous.

Record metadata

Canonical name: Topological group
Concept ID: topological_group
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Topology
Domains: Topology, Algebra, Algebraic topology
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

set $G$

Data

group structure
topology

Axioms / constraints

continuous multiplication
continuous inversion

Concept sources

Wikipedia — Topological group — Topological group · expository · source ID wp-top-group
nLab — Topological group — Topological group · reference · source ID nlab-top-group
Morris — Topology Without Tears — Topology Without Tears · textbook · source ID topology-without-tears

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

group + topology(construction junction)Topological group

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: e_jtg_tg
Relation type: Combine compatible structures combine-compatible
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + continuity

Authored explanation

Require multiplication and inversion to be continuous.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Wikipedia — Topological group — Topological group · expository · source ID wp-top-group
nLab — Topological group — Topological group · reference · source ID nlab-top-group
Morris — Topology Without Tears — Topology Without Tears · textbook · source ID topology-without-tears

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.