2011 | OriginalPaper | Chapter
Linear Spaces
Author : Prof. Dr. Johannes Jahn
Published in: Vector Optimization
Publisher: Springer Berlin Heidelberg
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Although several results of the theory described in the second part of this book are also valid in a rather abstract setting we restrict our attention to real linear spaces. For convenience, we summarize in this chapter the well-known definitions of linear spaces and convex sets as well as the definition of (locally convex) topological linear spaces and we consider a partial ordering in such a linear setting. Finally, we investigate some special partially ordered linear spaces and list various known properties.