Summary
In this introductory chapter we look at ordinary convexity in ℝn by embedding ℝn into real projective space ℝℙn. In this way convexity becomes invariant under projective mappings. In Section 1.1 we discuss very briefly conditions that characterize convexity in ℝn. In Section 1.2 we introduce fundamental geometric concepts in real projective space ℝℙn such as projective lines, projective hyperplanes and projective mappings. In Section 1.3 we define convexity in ℝℙn and study fundamental properties of convex sets. We define the polar of a subset in ℝℙn and relate convex sets and linearly convex sets.
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© 2004 Springer Basel AG
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Andersson, M., Sigurdsson, R., Passare, M. (2004). Convexity in Real Projective Space. In: Complex Convexity and Analytic Functionals. Progress in Mathematics, vol 225. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7871-5_1
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DOI: https://doi.org/10.1007/978-3-0348-7871-5_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9605-4
Online ISBN: 978-3-0348-7871-5
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