On the extreme points of the sum of two compact convex sets

1970 ◽  
Vol 188 (2) ◽  
pp. 113-122 ◽  
Author(s):  
T. Husain ◽  
I. Tweddle
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Extreme Points

scholarly journals Linear metric spaces and analytic sets

1994 ◽  
Vol 37 (2) ◽  
pp. 355-358
Author(s):  
Robert Kaufman
Keyword(s):  
Set Theory ◽  
Convex Sets ◽  
Metric Spaces ◽  
Compact Convex ◽  
Extreme Points ◽  
Descriptive Set Theory ◽  
Analytic Sets ◽  
Descriptive Set

A problem in descriptive set theory, in which the objects of interest are compact convex sets in linear metric spaces, primarily those having extreme points.

scholarly journals Mazur's intersection property of balls for compact convex sets

1987 ◽  
Vol 35 (2) ◽  
pp. 267-274 ◽  
Author(s):  
J. H. M. Whitfield ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Uniform Convergence ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Intersection Property ◽  
Compact Sets ◽  
Compact Convex Set ◽  
Mazur's Intersection Property

We show that every compact convex set in a Banach space X is an intersection of balls provided the cone generated by the set of all extreme points of the dual unit ball of X* is dense in X* in the topology of uniform convergence on compact sets in X. This allows us to renorm every Banach space with transfinite Schauder basis by a norm which shares the mentioned intersection property.

On compact convex sets with given extreme points

1995 ◽  
Vol 36 (1) ◽  
pp. 17-23
Author(s):  
E. M. Bronshtein
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Extreme Points

scholarly journals Extreme points and geometric aspects of compact convex sets in asymmetric normed spaces

2016 ◽  
Vol 203 ◽  
pp. 12-21 ◽  
Author(s):  
Natalia Jonard-Pérez ◽  
Enrique A. Sánchez Pérez
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Extreme Points ◽  
Normed Spaces
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