Spaces of remote points

Given a Tychonoff space X, let ϱ ( X ) be the set of remote points of X. We view ϱ ( X ) as a topological space. In this paper we assume that X is metrizable and ask for conditions on Y so that ϱ ( X ) is homeomorphic to ϱ ( Y ) . This question has been studied before by R.G. Woods and C. Gates. We give some results of the following type: if X has topological property P and ϱ ( X ) is homeomorphic to ϱ ( Y ) , then Y also has P. We also characterize the remote points of the rationals and irrationals up to some restrictions. Further, we show that ϱ ( X ) and ϱ ( Y ) have open dense homeomorphic subspaces if X and Y are both nowhere locally compact, completely metrizable and share the same cellular type, a cardinal invariant we define.