Abstract. We give a simple example of a regular space which is not completely regular.

Recently H. Herrlich has raised the question whether there exists a single Moore space Y such that every Moore space can be embedded into some topological power of Y. We answer this question negatively by proving the theorem stated in the title.

A short proof is given of an internal characterization of completely regular spaces due to J. Kerstan.

ABSTRACT.We present simple examples of a realcompact zerodimensional space which is not Ar-compact and an N-compact space which is not strongly zerodimensional.

No abstract