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Canonical static concept record

Real-analytic manifold

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Summary

A manifold whose chart transitions are real-analytic.

Record metadata

Canonical name: Real-analytic manifold
Concept ID: real_analytic_manifold
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Differential geometry
Domains: Differential geometry, Analysis, Topology
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

topological manifold $M$

Data

compatible real-analytic atlas

Axioms / constraints

transition maps are real-analytic

Canonically induces

A smooth manifold

Notes

A real-analytic atlas refines the smooth structure. The analytic structure is extra data; the underlying smooth structure is canonically obtained by forgetting analyticity.

Concept sources

Wikipedia — Analytic manifold — Analytic manifold · expository · source ID wp-analytic-manifold
Lee — Introduction to Smooth Manifolds — Introduction to Smooth Manifolds · textbook · source ID lee-smooth-manifolds

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Smooth manifold Real-analytic manifold

Permalink to relation

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

Relation ID: smooth_to_analytic
Relation type: Add data add-data
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + compatible analytic atlas

Authored explanation

Choose a real-analytic atlas compatible with the underlying smooth structure.

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Wikipedia — Analytic manifold — Analytic manifold · expository · source ID wp-analytic-manifold
Lee — Introduction to Smooth Manifolds — Introduction to Smooth Manifolds · textbook · source ID lee-smooth-manifolds

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.

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