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Cardinality of some convex sets and of their sets of extreme points

Zbigniew Lipecki (2011)

Colloquium Mathematicae

We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that = . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).

Cartesian Products of Family of Real Linear Spaces

Hiroyuki Okazaki, Noboru Endou, Yasunari Shidama (2011)

Formalized Mathematics

In this article we introduced the isomorphism mapping between cartesian products of family of linear spaces [4]. Those products had been formalized by two different ways, i.e., the way using the functor [:X, Y:] and ones using the functor "product". By the same way, the isomorphism mapping was defined between Cartesian products of family of linear normed spaces also.

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