Positive Bases for Linear Spaces
Richard L. McKinney · Transactions of the American Mathematical Society · 1962
A is denoted by card A. L will denote an arbitrary real linear space.Elements of L will be represented by lower case letters, excluding r, s and t, which will usually represent real numbers, and i, j, k, l, m and n, which will denote integers.The neutral element of L will be denoted by 0, the empty set by A, and real-valued functions by Greek letters. Positively Spanning Sets and Semispaces1.1.Introduction.For a subset A oí L, let 8A be the set of all real valued functions on A which vanish (i.e., have value 0) at all but a finite number of points of A. Denote by fyA the set of all non-negative members of 2A, i.e., those members of %A which are non-negative at each point of A. For XE&4, let X0 be the value of X at a.For X£&4, we shall say that a appears in X if and only if X^O.If a appears in X we shall also say that X involves a.A linear