Abstract
This chapter is of preliminary character. It contains a study of sets and functions with respect to cones in infinite dimensional spaces. First, we give definitions concerning convex cones and properties of cones with special structure such as correct cones and cones with convex bounded base. In Section 2, we introduce the concept of recession cones of nonconvex sets which plays an important role in nonconvex optimization. The next four sections deal with sets and functions in the spaces with the presence of convex cones. The last section provides some definitions and results about set-valued maps which will be needed in the study of optimization problems with set-valued data.
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