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

Ofelia T. Alas

Brazil

Universidade de Sao Paulo

Instituto de Matemática e Estatística

Richard G. Wilson

Mexico

Universidad Autónoma Metropolitana

Departamento de Matemáticas
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Accepted: 2013-11-28

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

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

Supporting agencies:

Consejo Nacional de Ciencia y Tecnología (México)

grant 38164-E and Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo (Brasil)

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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References:

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