Positive bases for linear spaces

spaces. We begin by considering various characterizations of positively spanning sets. Some of these will be of a geometric nature, and lead to consideration of the semi-spaces first defined by Hammer [3]. ?2 is concerned with positive bases and their dependence on certain minimal subspaces. Generalizing a method of Davis, we are able in ?3 to characterize positive bases as linearly spanning sets which admit a certain type of real function. Finally, in ?4, we show that even though an arbitrary positive basis may lack certain desirable properties possessed by linear bases, there are special classes of positive bases which do have some of these properties.