Some generalizations of universal mappings
A mapping \(f: X\to Y\) is universal if for each mapping \(g:X\to Y\) there is a point \(x\) in \(X\) such that \(f(x)= g(x)\). The author defines several variations of the concept, as semi-universal, weakly universal and pseudo-universal mappings, and establishes relationships between these classes of mappings, the fixed point property, the span of continua and the Borsuk-Ulam theorem. Reviewer's remarks: Theorem 4 (the composition of semi-universal mappings is semi-universal) and Theorem 6 (each inessential mapping \(f:X\to S^1\) is semi-universal) are false. Theorem 6 should be replaced by: ``each inessential mapping \(f:X\to S^1\) is weakly universal''. An appropriate ``Errata'' has been sent to the journal by the author.
scientific article; zbMATH DE number 1206694
scientific article