Topological Rings and Infinite Matrices |
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abelian topological group addition axiom of countability bourhood called closed columns compact complete condition consider contains continuous function converges correspondence correspondence is continuous countability axiom d₂ defined definition 2.9 denote described elements evidently exists a neighbourhood field finite form a basis Furthermore G₂ given group with operator Hausdorff space hence homomorphism hood ideal implies infinite basis infinite matrices infinitely non-zero integers introduced inverse isomorphic known lemma Let G linear mean multiplication namely neigh neighbour non-singular non-singular matrices noted obtain operator ring Pontrjagin prime Proof properties prove readily representation represents require respectively restrictions ring of infinite ring of operators satisfying the second second axiom sequence shown simple subset taking theorem theorem 4.1 thesis topological ring unique unit University of Wisconsin variable vector space well-known whence whole written zero