On some abstract convexity notions in real linear spaces

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. Mathematics subject classification (2000): 15A03, 52A01, 52A41.