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
In Branch
Source Namioka's theorem - Wikipedia
Proved By
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
Proved By: Isaac Namioka, Lead
Isaac Namioka, who proved it in his 1974 paper Separate Continuity and Joint Continuity published in the Pacific Journal of Mathematics, the theorem establishes conditions under which a separately continuous function must be jointly continuous on a topologically large subset of its domain.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.