Index B(a,r), see also open ball B(a, r), see also closed ball expp, see also p-adic exponential Fv, 113 Gs, 113 lnp, see also p-adic logarithm N, see also natural numbers Q, see also rational numbers Qp, see also p-adic numbers M, see also real numbers Z, see also integers Zp, see also p-adic integers Z* , see also p-adic units absolute value, 3 Baire Category Theorem, 114 Bolzano-Weierstrass Theorem, 26 canonical p-adic expansion, 24 canonical form of a p-adic number, see also canonical p-adic expansion Cantor diagonal process, 62 Cantor set, 60 middle thirds, 64 Cantor's Theorem, 56 capacity, 122 closed ball, 4 commutative ring, 6, 39 Completion Theorem, 2 congruent modulo pn, 34 convex hull, 72 derivative, 84 Dirichlet function, 112 distance induced by the norm, 7 distance function, see also metric equivalent Cauchy sequences, 2, 16 metrics, 9 norms, 9 Euclidean distance, 3 Euclidean models of Zp, 69 Euclidean norm, see also absolute value Euler's Theorem, 42 fat Cantor set, 64 Fermat's Little Theorem, 43 field, 6 additive group of, 6 multiplicative group of, 6 first difference quotient, 119 function characteristic, 103 continuous, 63, 103 differentiable, 84 locally constant, 104 oscillation of, 113 strictly differentiable, 119 uniformly continuous, 103 group abelian, 6 Hadamar's formula, 81 Hasse-Minkowski Theorem, 47 Heine-Borel Theorem, 58 Hensel's Lemma, 34 Holder condition, 117 homeomorphism, 63 151

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