I was asked whether this is true in a question paper: If p is a subset of q (where both p & q are convex), then an extreme point of q is also an extreme point of p. Ans.: Yes statement is correct.
I disagree: take two squares with q larger than p. An extreme point of q is not contained in p. So, this point is the empty set when we are considering p since p does not contain it. Since an empty set does not contain a point, statement is false.
The definition of extreme point itself starts with nonempty convex sets.
Why first statement above is correct?
Note:I posted this on overflow but was told that it's mainly a place for research questions and this one surely isn't. thx