Namioka's theorem, proved by the mathematician Isaac Namioka in a 1974 paper in the Pacific Journal of Mathematics, is a result in functional analysis concerning the relationship between separate and joint continuity of functions defined on product spaces. It establishes conditions under which a function that is continuous in each variable separately must in fact be jointly continuous on a topologically large subset of its domain.
Facts
StatementConditions under which a separately continuous function must be jointly continuous on a topologically large subset of its domain. 1 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
Source Namioka's theorem - Wikipedia
Sources
1. Namioka's theorem - Wikipedia
Introduction, sentence 2, main clause
the theorem establishes conditions under which a separately continuous function must be jointly continuous on a topologically large subset of its domain.
Introduction, sentence 2, relative clause
who proved it in his 1974 paper
In Branch: Functional Analysis, Lead sentence
In functional analysis, Namioka's theorem is a result concerning the relationship between separate continuity and joint continuity
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