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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

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1 Answer 1

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.

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