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Journal of Convex Analysis 21 (2014), No. 2, 581--600
Copyright Heldermann Verlag 2014

Convex Closures, Weak Topologies and Feeble Approach Spaces

Robert Lowen
University of Antwerp, Dept. of Mathematics and Computer Science, Middelheimlaan 1, 2020 Antwerp, Belgium

Sevda Sagiroglu
Dept. of Mathematics, University of Ankara, Ankara, Turkey

We develop a setting within the realm of approach theory to be able to deal with the non-topological notion of closed convex closure in an isometric way. We work out the necessary machinery and show how closed convex and weak* closed convex closure and the weak and weak* topologies in normed spaces fit into the framework.

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