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Every needle point space contains a compact convex AR-set with no extreme points


Authors: Nguyen To Nhu and Le Hoang Tri
Journal: Proc. Amer. Math. Soc. 120 (1994), 1261-1265
MSC: Primary 54C55; Secondary 54D45
DOI: https://doi.org/10.1090/S0002-9939-1994-1152989-0
MathSciNet review: 1152989
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Abstract: Every needle point contains a compact convex AR-set without any extreme points. In particular the following spaces contain such compact convex sets: (i) the spaces $ {L_p},\;0 \leqslant p < 1$; (ii) the linear metric space constructed by Roberts (Studia Math. 60 (1977), 255-266).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1152989-0
Keywords: Needle point, needle point space, extreme point, convex set, AR, fixed point property, Hilbert cube, admissible convex set
Article copyright: © Copyright 1994 American Mathematical Society

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