RT Journal Article
T1 The Hausdorff Metric and Classifications of Compacta
A1 Alonso Morón, Manuel
A1 González Gómez, A.
AB In this paper we use the Hausdorff metric to prove that two compact metric spaces are homeomorphic if and only if their canonical complements are uniformly homeomorphic. So, we take one of the two steps needed to prove that the difference between the homotopical and topological classifications of compact connected ANRs depends only on the difference between continuity and uniform continuity of homeomorphisms in their canonical complements, which are totally bounded metric spaces. The more important step was provided by the Chapman complement and the Curtis-Schori-West theorems. We also improve the multivalued description of shape theory given by J. M. R. Sanjurjo but only in the class of locally connected compacta.
PB London Mathematical Society
SN 1469-2120
YR 2006
FD 2006
LK https://hdl.handle.net/20.500.14352/50514
UL https://hdl.handle.net/20.500.14352/50514
LA deu
NO Alonso Morón, M., y González Gómez, A. «THE HAUSDORFF METRIC AND CLASSIFICATIONS OF COMPACTA». Bulletin of the London Mathematical Society, vol. 38, n.o 02, abril de 2006, pp. 314-22. DOI.org (Crossref), https://doi.org/10.1112/S0024609305018382.
NO Directorate General for Higher Education (Portugal)
DS Docta Complutense
RD 8 abr 2025