Describes how the fundamental group of a topological space formed by gluing two open, path-connected pieces together can be computed from the fundamental groups of the two pieces and of their overlap. Named for Egbert van Kampen, it is a basic computational tool of algebraic topology.
Facts
StatementThe fundamental group of a topological space that is the union of two open, path-connected subspaces whose intersection is path-connected and nonempty can be computed from the fundamental groups of the two subspaces and of their intersection. 1 Proof YearHerbert Seifert proved a related special case independently in 1931; van Kampen's 1933 paper is the namesake general result. Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
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
Sources
1. Van Kampen's Theorem (Wikipedia)
Wikimedia FoundationReferences sectionQuote, References section
E. R. van Kampen. On the connection between the fundamental groups of some related spaces. American Journal of Mathematics, vol. 55 (1933), pp. 261-267.
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