Countable dense homogeneity and the Baire property
A separable space \(X\) is called countable dense homogeneous (CDH) if for all countable dense subsets \(A\) and \(B\) of \(X\) there is an autohomeomorphism \(h\) of \(X\) with \(h[A]=B\). In this paper the authors discuss countable dense homogeneity in relation with the Baire property. They show among other things that it is consistent with ZFC that every CDH metric space \(X\) of cardinality \({\mathfrak c}\) is nonmeager. They also show that under CH there is a meager CDH subspace of the real line. Hence it is independent with ZFC that there is a meager CDH metric space of size \({\mathfrak c}\).
meager countable dense homogeneous metric space
scientific article; zbMATH DE number 60701
scientific article