Algebraic TopologyAmerican Mathematical Society, 1942 - 389 pages A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \{e^{{{i\lambda}_n} x}\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie. |
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CHAPTER PAGE | 1 |
ADDITIVE GROUPS | 41 |
COMPLEXES | 88 |
Droits d'auteur | |
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acyclic base Betti numbers carrier Čech chain-homotopic chain-mapping chains closed sets closed subcomplex cocycles coefficients cofinal cohomology combinatorial compactum component consequence contains coordinates corresponding coset countable cycles defined definition denote dimension discrete disjoint dual duality theorems dually paired elements equivalent Euclidean complex finite complexes finite number finite open coverings follows G₁ group G H₁ Hausdorff space hence Hilbert parallelotope holds homology groups homology theory homomorphism homotopy incidence numbers induces infinite integral intersection isomorphism K₁ Kronecker index Let G likewise linearly compact linking coefficient manifolds mapping metric multiplication neighborhood notations open covering open sets orientable p-cycle projection proof properties prove relation replaced simplex simplicial complex subgroup subset subspace Suppose T₁ topological group topological space torsion coefficients transformation U₁ V₁ vector spaces vertex vertices Vietoris X₁ Y₁ zero zero-cyclic