RT Journal Article
T1 Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology
A1 González Gómez, A.
A1 Alonso Morón, Manuel
AB In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the Cˇ ech–Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject.
PB Elsevier Science
SN 0166-8641
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50510
UL https://hdl.handle.net/20.500.14352/50510
LA eng
NO Alonso Morón, M., y González Gómez, A. «Upper Semifinite Hyperspaces as Unifying Tools in Normal Hausdorff Topology». Topology and Its Applications, vol. 154, n.o 10, mayo de 2007, pp. 2142-53. DOI.org (Crossref), https://doi.org/10.1016/j.topol.2006.03.031.
DS Docta Complutense
RD 12 abr 2025