Kakutani property of the polytopes implies Kakutani property of the whole space

DOI10.1016/0022-247X(88)90388-5zbMath0646.54044MaRDI QIDQ1103911

Klaus Keimel, Andrzej Wieczorek

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

polytopescompactificationsKakutani fixed point theoremcontinuous latticesclosed convex subsetsupper semicontinuous set-valued map

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Fixed-point and coincidence theorems (topological aspects) (54H25) Topological lattices, etc. (topological aspects) (54H12)

Related Items (5)

Some general principles in tropical convexities ⋮ Topological convexities, selections and fixed points ⋮ Compressibility: A property of topological spaces related to abstract convexity ⋮ The Kakutani property and the fixed point property of topological spaces with abstract convexity ⋮ Joint pseudo-utility representations

Cites Work

• Euclidean convexity cannot be compactified
• Verallgemeinerter Konvexitätsbegriff und der Satz von Krein-Milman
• Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
• A Quick Proof for a One-Dimensional Version of Liapounoff's Theorem
• CUT POINTS IN GENERAL TOPOLOGICAL SPACES
• A Further Generalization of the Kakutani Fixed Point Theorem, with Application to Nash Equilibrium Points
• Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
• A Note on Dendrites and Trees
• A fixed-point theorem for trees
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