Compactifications with Countable Remainder

M. G. Charalambous
1980 Proceedings of the American Mathematical Society  
In this paper, we deal with the problem of characterizing those spaces that have a compactification with countable remainder. A result. Theorem. Let X be a Cech-complete, rim-compact space such that R(X) has a countable network. Then X has a countable compactification. Proof. Since X is rim-compact, X has at least one compactification Z with ind(Z -X) < 0, where ind denotes small inductive dimension, and since A"
doi:10.2307/2043054 fatcat:jq2jkfwr5zcf7ejbx7frzdmh3y