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Support functions and subdifferentials

Grzybowski J., Pallaschke D., Urbański R.

Commentationes Mathematicae

2016

Vol 56, No. 1

45--53

In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.

The spaces of closed convex sets in Euclidean spaces with the fell topology

Sakai K., Yang Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 2

139-143

Let ConvF(Rn) be the space of all non-empty closed convex sets in Euclidean space Rn endowed with the Fell topology. We prove that ConvF(lRn) ≈ Rn x Q for every n > 1 whereas ConvF(R) ≈ R x I.