I'm trying to show that the Least Core of is a convex set whenever is a convex and closed set in a topological vector space.

The definition of the Least Core is:

Where is the maximum operator and M is the index set of all the funtions on

But what is the definition of a convex subset of a topological space that I should use?

Can I just use this notion:

Let be a vector space (over R or C). A subset S of V

is convex if for all points x,y in S, the line segment

is also in S.

Btw this is no homework, so I don't know exactly what definition to use.