Vol. 98, No. 2, 1982

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Barycentric simplicial subdivision of infinite-dimensional simplexes and octahedra

Thomas E. Armstrong

Vol. 98 (1982), No. 2, 251–270

A K-simplex is a convex set affinely homeomorphic to the positive face of the unit ball of a Kakutani L-space and an octahedron is a convex set affinely homeomorphic to the entire unit ball. It is shown how to barycentrically subdivide K-simplexes and octahedra so that the K-simplexes in the subdivision are affinely homeomorphic to the simplexes of probability measures on closed subsets of (0,) with the weak topology. As a consequence, for any closed subset C of (0,), an apparently new complete metric for the weak topology on 1+(C) is given.

Mathematical Subject Classification 2000
Primary: 46A55
Secondary: 46E30, 52A07
Received: 5 August 1980
Revised: 11 February 1981
Published: 1 February 1982
Thomas E. Armstrong