4 papers · 1 filter
The number of translates of a closed nowhere dense set required to cover a Polish group
Arnold W. Miller, Juris Steprans
For a Polish group G let cov_G be the minimal number of translates of a fixed closed nowhere dense subset of G required to cover G. For many locally compact G this cardinal is know…
Half of an inseparable pair
Arnold W. Miller
A classical theorem of Luzin is that the separation principle holds for the Pi^0_alpha sets but fails for the Sigma^0_alpha sets. We show that for every Sigma^0_alpha set A which i…
The cardinal characteristic for relative gamma-sets
Arnold W. Miller
For a separable metric space define $\pp(X)$ to be the smallest cardinality of a subset of which is not a relative $\ga$-set in , i.e., there exists an $\om$-cover o…
On squares of spaces and Fsigma-sets
Arnold W. Miller
We show that the continuum hypothesis implies there exists a Lindelof space X such that X x X is the union of two metrizable subspaces but X is not metrizable. This gives a consist…