On generalized Erdős spaces

Abstract

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.

One-Point Connectifications

“…Among more recent results we mention that of M. Abry, J.J. Dijkstra, and J. van Mill in [1] stating that a separable metrizable space in which every component is open has a separable metrizable one-point connectification if and only if it has no compact component. Other results concerning connectifications of spaces may be found in [2], [5], [6], [7], [9], [12], [14], [22], [34] and [38]. For results concerning general one-point extensions of spaces see [20] and [23] and the cited bibliography therein.…”