Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658260 | Topology and its Applications | 2015 | 11 Pages |
Abstract
It is a result of A. Bouziad that every regular, first countable, totally imperfect space with no isolated points is not Fin-trivial. We prove that every regular totally imperfect space containing a copy of the rational numbers is not Fin-trivial in a strong sense. Our result generalizes that of Bouziad to a larger class of spaces and gives a strengthened conclusion. As a corollary we conclude that various splitting topologies on the space of continuous real-valued functions defined on a metric space need not coincide.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Francis Jordan,