Barycentric simplicial subdivision of infinite-dimensional simplexes and octahedra

Thomas E. Armstrong

Vol. 98 (1982), No. 2, 251–270

DOI: 10.2140/pjm.1982.98.251

Abstract

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 ℳ₁⁺(C) is given.

Mathematical Subject Classification 2000

Primary: 46A55

Secondary: 46E30, 52A07

Milestones

Received: 5 August 1980

Revised: 11 February 1981

Published: 1 February 1982