Inverse systems and I-favorable spaces (Q958511)

An I-favorable topological space is defined by means of a winning strategy in a open-open selection game. It is proved that an inverse limit of a \(\sigma\)-complete inverse system of spaces having countable \(\pi\)-bases with skeletal (almost open) bonding maps and surjective projections is I-favorable. The converse is true for compact spaces -- the spaces in the inverse system can be chosen to be compact metrizable. Especially, Shchepin's compact \(\kappa\)-metrizable spaces are I-favorable.