@article{Alas_Wilson_2011, title={The structure of the poset of regular topologies on a set}, volume={12}, url={https://polipapers.upv.es/index.php/AGT/article/view/1695}, DOI={10.4995/agt.2011.1695}, abstractNote={<p>We study the subposet E<sub>3</sub>(X) of the lattice L<sub>1</sub>(X) of all T<sub>1</sub>-topologies on a set X, being the collections of all T<sub>3</sub> topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E<sub>3</sub>. We also consider the problem of when an R-closed topology is maximal R-closed.</p>}, number={1}, journal={Applied General Topology}, author={Alas, Ofelia T. and Wilson, Richard G.}, year={2011}, month={Apr.}, pages={1–13} }