The Theory of Topological Commutative Groups.¶
Pontryagin, L. S. (1934). The Theory of Topological Commutative Groups. Annals of Mathematics, 361-388.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Duality
- … in dual form (where the Lagrangian dual and the LP dual are the canonical industrial cases), logical operations in one vocabulary (∧, ∀) translate mechanically to the other (∨, ∃) via De Morgan's laws, topological and algebraic categories (Boolean algebras ↔ Stone spaces, locally-compact groups ↔ character groups
This sourceEstablished the duality between a locally compact abelian group and its character group. Textbook treatment: Pontryagin, Topological Groups (Princeton UP, 1939; English trans. 1946); Rudin, Fourier Analysis on Groups (Wiley, 1962).
- … in dual form (where the Lagrangian dual and the LP dual are the canonical industrial cases), logical operations in one vocabulary (∧, ∀) translate mechanically to the other (∨, ∃) via De Morgan's laws, topological and algebraic categories (Boolean algebras ↔ Stone spaces, locally-compact groups ↔ character groups
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Not recorded. The single citation of this work carries no recorded support check.
Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:ef79102fa0e1 · see in the full table