Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777693 | Topology and its Applications | 2017 | 5 Pages |
Abstract
We prove that there is no regular maximal connected expansion of the Euclidean topology ε on the set R of real numbers. For this, we first consider a Hausdorff connected submaximal space (R,Ï) with εâÏ and then, with the aid of the filter of the Ï-dense sets, we define two specific expansions Ï,Ïâ of ε, such that ÏââÏ,ÏââÏ and (R,Ï) is submaximal. We prove that if (R,Ï) is in addition nearly maximal connected, then Ï=Ïâ. Finally we prove that (R,Ï) cannot be regular.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
A. Kalapodi, V. Tzannes,