Non-Archimedean Functional Analysis |
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algebraically closed Archimedean Banach space BC(X BUC(X C-algebra choose clopen closed linear subspace compact open subgroup compact space compact subgroup contains continuous linear COROLLARY cosets countable type covering ring define denote dense dimensional discrete equivalent EXERCISE finite group G Haar measure Hausdorff space Hence idempotent induces isometry isomorphism KIXI left Haar measure left invariant measure LEMMA Let G linear hull linear isometry linear map linear subspace locally compact zerodimensional maximal ideal N-compact natural map non-Archimedean non-Archimedean uniformity non-Archimedean valued field non-measurable non-zero normed vector space orthogonal base orthogonal system orthonormal partition polynomial PROOF prove q-free q-free compact quotient R-continuous reflexive residue class field semigroup sequence spherically complete subgroup H subgroup of G subgroup topology subset surjective THEOREM theory topological group topological space torsional group ultrametric ultrametrizable unit element valuation value group zerodimensional Hausdorff space