Authors: Vatolin Dm.
Comments: 11 Pages. Russian
The proof of the Cantor hypothesis about the continuum power is found. Since previously quite convincing axioms that are not compatible with the continuum hypothesis were discovered, the relationships between the «Cantor» and «non-Cantor» sets are analyzed.
Authors: Pierre-Yves Gaillard
Comments: 4 Pages.
To a topological space X we attach in two equivalent ways a profinite space X' and a continuous map F: X --> X' such that, for any continuous map f: X --> Y, where Y is a profinite space, there is a unique continuous map f': X' --> Y such that f'oF = f.