Abstract. Erdős space E is the 'rational' Hilbert space, that is the set of vectors in 2 the coordinates of which are all rational. Erdős proved that E is one-dimensional and homeomorphic to its own square E × E, which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of E. Let M n+1 n , n ∈ N, be the n-dimensional Menger continuum in R n+1 , also known as the ndimensional Sierpiński carpet, and let D be a countable dense subset of M

During the last years both Erdős space and complete Erdős space were topologically characterized by Dijkstra and van Mill. Applications include results about Erdős type spaces in p-spaces as well as results about Polishable ideals on ω. We present an unifying theorem in terms of sets with a reflexive relation that among other things contains these apparently dissimilar results as special cases.