 
Summary: 1. Preliminaries.
1.1. Tangents and normals.
Definition 1.1. Suppose A Rn
and a is an accumulation point of A. For each
r (0, ) we let
Ta,r(A) = cl {t(x  a) : 0 < t < and x B(a, r) {a}}
and note that Ta,r is a closed cone with vertex 0 in Rn
. We let
Ta(A) =
0
Ta,r(A).
We let
Na(A) = {v Rn
: v · w 0 whenever v Ta(A)}.
1.2. gi,j and gi,j
.
Exercise 1.1. Suppose V is an mdimensional inner product space; v is a basic
sequence for V ; is the corresponding dual basic sequence for V
; i V
, i =
