TY - JOUR
AU - Alas, Ofelia T.
AU - Wilson, Richard G.
PY - 2011/04/01
Y2 - 2023/03/23
TI - The structure of the poset of regular topologies on a set
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 12
IS - 1
SE -
DO - 10.4995/agt.2011.1695
UR - https://polipapers.upv.es/index.php/AGT/article/view/1695
SP - 1-13
AB - <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>
ER -