Do minimal pairs of convex sets exist?

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We already know

Let A and B be nonempty bounded closed convex sets in X. If X is a reflexive Banach space or A and B are compact sets then there exists minimal pair (C,D) smaller than (A,B).

In X=co,c and l [infinity] there exists a pair of bounded closed convex sets (A,B) that does not have equivalent minimal pair. Example:
A = { (a n)[is an element of]co | 0[less then or equal to] a n[less then or equal to]1, n [is an element of] N }, B = - A
Do you have a question?
Write to rich@amu.edu.pl ,
lh09@rz.uni-karlsruhe.de




We still do not know

Does there exist in every nonreflexive space X a quotient class [A,B] that contains no minimal pairs?
Do you have an answer?
Write to rich@amu.edu.pl,
lh09@rz.uni-karlsruhe.de


* Do minimal pairs of convex sets exist? * Are minimal pairs of compact sets unique? *
* What about convex polytops? * What are invariants of minimal pairs of convex sets? *
* How do minimal pairs of convex sets relate to fractions? *
* History of minimal pairs of convex sets *
* How did we get interested in pairs of convex sets? *
* References * Definitions *
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