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SEPARATION OF CONVEX SETS IN EXTENDED NORMED SPACES
Published online by Cambridge University Press: 26 February 2015
Abstract
We give continuous separation theorems for convex sets in a real linear space equipped with a norm that can assume the value infinity. In such a space, it may be impossible to continuously strongly separate a point $p$ from a closed convex set not containing $p$, that is, closed convex sets need not be weakly closed. As a special case, separation in finite-dimensional extended normed spaces is considered at the outset.
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- © 2015 Australian Mathematical Publishing Association Inc.
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