Alas, Ofelia T.Wilson, Richard G.2017-09-112017-09-112011-04-011576-9402https://riunet.upv.es/handle/10251/86961[EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 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 E3. We also consider the problem of when an R-closed topology is maximal R-closed.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Lattice of T1-topologiesPoset of T3-topologiesUpper topologyLower topologyR-closed spaceR-minimal spaceSubmaximal spaceMaximal R-closed spaceDispersed spaceThe structure of the poset of regular topologies on a setArtÃculo2017-09-1110.4995/agt.2011.1695Abierto1989-4147