A remark on universal marked spaces

By marked space we mean a pair (X, aX), where X is a topological space and aX is a fixed point of X. By embedding of a marked space (Y, aY) into a marked space (X, aX) we mean an embedding i of Y into X for which i(aY) = aX. In this paper it is proved that: (1) in the class of all marked spaces there are universal elements and (b) in the Alexandroff cube F? there are points a, such that the marked space (F?, a) is universal in the class of all marked spaces (note that not all points of F? satisfy this condition), which are answers to the corresponding problems, putting in [3].