Extension of continuous functions in 𝛽𝐍

Abstract

1. Introduction. The present considerations arose from the following problem: let j3N -N; is /3N -N-{p} C*-embedded in jSN-N-i.e., is j3(/3N-N-{p}) equal to /3N-N? 3 We prove, assuming the continuum hypothesis (designated by [CH]), that the answer is negative. More generally, see Theorem 4.6. The corresponding question for {5D y where D is any discrete space, is discussed in 5. The proofs depend upon results about /^-spaces. We also prove [CH] that all open subsets of /3R -R are F-spaces and that all open subsets of /3N -N are zero-dimensional ^-spaces.