Theorem

Cousin's Theorem

Analysis

Cousin's theorem is a result in real analysis. It states that if every point of a closed region is assigned a circle of finite radius, then the region can be divided into finitely many subregions, each of which lies inside one of a given set of circles and contains that circle's center. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts

Classification

Statement Form

Existence Theorem 1

Proof Year

1895 1

Connections

Has Statement Form

Existence Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Real Analysis

Source Cousin's Theorem (Wikipedia)

Sources

1. Cousin's Theorem (Wikipedia)

Lead paragraph
originally proved by Pierre Cousin, a student of Henri Poincaré, in 1895
In Branch: Real Analysis, Lead sentence
In real analysis, a branch of mathematics, Cousin's theorem states that: If for every point of a closed region (in modern terms, "

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Cousin's Theorem

Has Statement Form

In Branch