Universal Mappings (in sense of ``Universal Spaces'')
by
S.D. Iliadis

By a mapping we mean a continuous mapping of a topological space into a topological space. Let f:X₀ --> Y₀ and g:X₁ --> Y₁ be two mappings. A pair (i, j), where i:X₁ --> X₀ and j:Y₁ --> Y₀ are embeddings, is said to be an embedding of the mapping g into the mapping f if f o i=j o g. A mapping f of a class ( \equiv set) F of mappings is said to be universal in F if for every g in F there exists an embedding of g into f.

Let A and B be two classes of spaces. Denote by F(A, B) the class of all continuous mappings f:X --> Y such that X in A and Y in B.

We will indicate some (well-known) classes A and B for which in the class F(A, B), as well as, in some (well-known) subclasses of F(A, B) there exist universal elements.

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caah-41.