Geodesic
Convex Closures, Weak Topologies and Feeble Approach Spaces
Journal of convex analysis, Tome 21 (2014) no. 2, pp. 581-6
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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. 
@article{JCA_2014_21_2_JCA_2014_21_2_a14,
     author = {R. Lowen and S. Sagiroglu},
     title = {Convex {Closures,} {Weak} {Topologies} and {Feeble} {Approach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {581--6},
     year = {2014},
     volume = {21},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a14/}
}
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R. Lowen; S. Sagiroglu. Convex Closures, Weak Topologies and Feeble Approach Spaces. Journal of convex analysis, Tome 21 (2014) no. 2, pp. 581-6. http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a14/