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