Universal elements for some classes of spaces (Q2881010)

This paper concerns dimension-like functions and their universality property. Motivated by the fact that the dimension function \(Dm\) introduced by \textit{A. K. O'Conner} [Acta Math. Hung. 55, No.1-2, 83--95 (1990; Zbl 0715.54024)] does not have the universality property, in their earlier paper [Topology Appl. 155, No. 17-18, 2196--2201 (2008; Zbl 1160.54022)], the authors introduced dimension-like functions with the universality property. Continuing along this line, the authors introduce three more new dimension-like functions whose domain is the class of all spaces and whose range is the class of all ordinals with two symbols \(-1\) and \(\infty\), and show that those dimension-like functions have the universality property.