Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
up vote 3 down vote accepted

I think there are a few words missing from the original statement. Probably they mean that any extreme point of $Q$ that belongs to $P$ is also an extreme point of $P$.

The italicized part is supposed to be assumed, I guess. Without it, the statement is obviously false, as you pointed out.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.