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
Previous Page Next Page