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

Ofelia T. Alas; Richard G. Wilson

doi:10.4995/agt.2004.1972

Authors

Ofelia T. Alas Universidade de Sao Paulo
Richard G. Wilson Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.4995/agt.2004.1972

Keywords:

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

Abstract

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.

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Author Biographies

Ofelia T. Alas, Universidade de Sao Paulo

Instituto de Matemática e Estatística

Richard G. Wilson, Universidad Autónoma Metropolitana

Departamento de Matemáticas

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