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Bot, Radu Ioan; Csetnek, Ernö Robert; Wanka, Gert : On some abstract convexity notions in real linear spaces

Bot, Radu Ioan ; Csetnek, Ernö Robert ; Wanka, Gert : On some abstract convexity notions in real linear spaces

Author(s):
Bot, Radu Ioan
Csetnek, Ernö Robert
Wanka, Gert
Title:
On some abstract convexity notions in real linear spaces
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 7, 2006
Mathematics Subject Classification:
52A01 [ Axiomatic and generalized convexity ]
15A03 [ Vector spaces, linear dependence, rank ]
52A41 [ Convex functions and convex programs ]
Abstract:
We introduce some abstract convexity notions in a real linear space and investigate which of the results from the convex analysis in topological vector spaces still work in a linear space. The differences between these abstract convexity notions and those established in spaces endowed with a topology are underlined by some examples.
Keywords:
abstract convexity, c-convex hull, c-convexity
Language:
English
Publication time:
5 / 2006