Linear Spaces

Johannes Jahn ()
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Johannes Jahn: Universität Erlangen-Nürnberg

Chapter Chapter 1 in Vector Optimization, 2011, pp 3-36 from Springer

Abstract: Abstract 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.

Keywords: Topological Space; Linear Space; Convex Cone; Nonempty Subset; Weak Topology (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-17005-8_1

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