A closed separable subspace of 𝛽𝑁 which is not a retract

Abstract

We shall exhibit a countable subset, X X , of N ∗ {{\mathbf {N}}^{\ast }} whose closure is not a retract of β N \beta {\mathbf {N}} . The points of X X are constructed in c c steps with the aid of an independent matrix of subsets of ω \omega .