On the functor p of probability measures
A closed subset A of a space X is called a Z-set if the identity map can be approximated arbitrarily closely by mappings from X to \(X\setminus A\). Denote by P the functor of probability measures, by Q the Hilbert cube. We say that a dense \(\delta\)-Z-set B in Q is a boundary set (we write B(Q)) if \(Q\setminus B\approx \ell_ 2\). If X is an infinite compact set and \(A_ 1\subseteq A_ 2\subseteq..\). are closed subsets of X such that \(\cup^{\infty}_{i=1}A_ i\) is everywhere dense in X and \(\cup^{\infty}_{i=1}A_ i\neq X\) then \((P(X),\cup^{\infty}_{i=1}P(A_ i))\approx (Q,B(Q))\) and \(P(X)\setminus \cup^{\infty}_{i=1}P(A_ i)\approx \ell_ 2.\) If A is open everywhere dense in an infinite compact space X with \(A\neq X\) then \((P(X),P(A))\approx (Q,B(Q))\) and \(P(X)\setminus P(A)\approx \ell_ 2\).
scientific article; zbMATH DE number 4194667