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Adjacency in subposets of the lattice of T 1-topologies on a set |
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| Authors: | Ofelia T. Alas Salvador Hernández Manuel Sanchis Michael G. Tkachenko Richard G. Wilson |
| Affiliation: | 7301. Instituto de Matemática e Estatística, Universidade de S?o Paulo, Caixa Postal 66281, 05311-970 S?o Paulo, Brasil 7302. Departament de Matemátiques, Universitat Jaume I, Campus del Riu Sec, 12071 Castelló de la Plana, Spain 7303. Departament de Matemátiques, Universitat Jaume I, Campus del Riu Sec, 12071 Castelló de la Plana, Spain 7304. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, México, D.F., México 7305. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, México, D.F., México |
| Abstract: | Summary We study subposets of the lattice L_1(X) of all T1-topologies on a set X, namely Σt(X), Σ3(X) and Σlc(X), being respectively the collections of all Tychonoff, all T3 and all locally compact Hausdorff topologies on X, with a view to deciding which elements of these partially ordered sets have and which do not have covers, that is to say immediate successors, in the respective posets. In the final section we discuss the subposet Σ G of all Hausdorff group topologies on a group G. |
| Keywords: | cover of a topology topological group topology lattice of T1-topologies adjacency of topologies |
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