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The Constructivization of Mathematics
The Real Number System
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approximation arbitrarily assume Banach algebra Banach space belongs bounded linear functional bounded subset called Cauchy sequence Chapter Choose r>0 commutative compact set compact subset compact support complemented set complete complex number Consider an arbitrary constructive continuous function convex Corollary countably defined Definition differentiable function double norm e>0 there exists elements equal equivalence finite finite-dimensional follows full set function g given Hence hermitian operators Hilbert space induced inequality integer integrable function integrable set integrable with respect integration space inverse J-full Lemma Let f linear map locally compact space mappable measurable functions metric space modulus of continuity neighborhood neZ+ nonnegative nonvoid nonzero norm-preserving normable linear functional normed linear space normed space notion open set pointwise positive integer positive measure Proof Proposition prove rational numbers real numbers relative simple function subfinite test function theorem theory topology totally bounded uniformly continuous unit sphere vector write