Which topologies can have immediate successors in the lattice of T1-topologies?

[EN] We give a new characterization of those topologies which have an immediate successor or cover in the lattice of T1-topologies on a set and show that certain classes of compact and countably compact topologies do not have covers.Research supported by Consejo Nacional de Ciencia y Tecnología (México), grant 38164-E and Fundacão de Amparo a Pesquisa do Estado de São Paulo (Brasil)Alas, OT.; Wilson, RG. (2004). Which topologies can have immediate successors in the lattice of T1-topologies?. Applied General Topology. 5(2):231-242. https://doi.org/10.4995/agt.2004.19722312425