1st December 2004
Munkres 11
Ex. 11.8 (Morten Poulsen). First recall some denitions: Let V be a vector space over a eld
K. Let A be a (possibly empty) subset of V . The subspace spanned by A is denoted spanK A and
is dened by
spanK A = cfw_ k1 a1 + + kn a

1st December 2004
Munkres 4
Ex. 4.2. We assume that there exists a set R equipped with two binary operations, + and , and
a linear order < such that
(1) (R, +, ) is a eld.
(2) x < y x + z < y + z and 0 < x, 0 < y 0 < xy
(3) (R, <) is a linear continuum
Us