Completely cell soluble spaces (Q1177331)

The author studies Arkhangel'skij's notion of cell solubility. Arkhangel'skij proved that a retract of a homogeneous compact Hausdorff space has this property. The author solves several problems of Arkhangel'skij by presenting among other things an example of a non- representable abstract cellularity and proving that every zero- dimensional compact Hausdorff space is completely cell soluble (thus generalizing for compact spaces the main result in [the author, Proc. Am. Math. Soc. 110, 569-571 (1990; Zbl 0776.54017)].