Topological Rings and Infinite Matrices |
Common terms and phrases
abelian topological group additive group axiom of countability bourhood columns compact and satisfy compact commutative group continuous function correspondence is continuous correspondence is preserved countability axiom countable set d₂ defined definition 2.9 denote exists a neighbourhood finitely non-zero rows form a basis G into G G₂ give all possible group with operator Hausdorff space homomorphism of G infinite basis infinite direct sum infinite matrices infinitely non-zero integers inuous lemma Let G linear subspace linear transformations matrices of M(V matrix theory neigh neighbourhood of zero neighbourhoods in G non-singular matrices open set operator homomorph operator ring possible orders preserved under addition principal diagonal principal ideal ring Proof real numbers ring of homomorphisms ring of infinite ring of matrices ring of operators Rings and Infinite satisfying the second second axiom sequence subring subset Suppose lim theorem 4.1 theory of infinite thesis topological ring U₂ University of Wisconsin vector space whence