A Note on Αcozero-complemented Spaces and Αborel Sets

α is a regular cardinal number or the symbol ∞, and X is a compact Hausdorff space. It is shown that (Theorem 2.1) X is αcozerocomplemented iff each αBorel set differs from an αcozero set by a meagre set. This immediately yields (Corollary 2.2) X is αdisconnected iff each αBorel set differs from a clopen set by a meagre set. (The cases α = ∞ in Theorem 2.1, and α = ω1 in Corollary 2.2 are important theorems in Boolean Algebra). The Boolean algebra of αBorel sets modulo meagre sets is considered as an extension of the clopen algebra on X (when X is Boolean), and compared with the αcut-completion and the αcompletion. (For α =∞, each of the three is the completion.)