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

Ofelia T. Alas, Richard G. Wilson


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.


Lattice of T1-topologies; Maximal point; KC-space; Cover of a topology; Upper topology; Lower topology

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