ABSTRACT
A continuum means a compact, connected Hausdorff space, and a mapping means a continuous transformation. A mapping / : X —> Y between topological spaces X and Y is said to be universal provided that it has a coincidence with every mapping from X into V, or — more precisely — provided that for every mapping g : X —> Y there exists a point x e X such that f ( x ) = g(x). The concept of a universal mapping has been introduced in [4, p. 603] by W. Holsztynski.
