Definition
Let X be a compactum i.e. an infinite compact Hausdorff space.
X is called an AB-compactum if the cofinality? of the character
is countable whenever Y is a subset of X and x is a point in Y.
Reference
Isaac Gorelic, Istvan Juhasz, AB-compacta, Comment. Math. Univ. Carolin. 49,1 (2008) 141–146.