Covering Relations in the Lattice of ^-topologies
نویسنده
چکیده
A topology ^"i is said to cover another topology T3 if ^Ç^i and no other topology may be included between the two. In this paper, we characterize the relationship between a Tj-topology and its covers. This characterization is used to prove that the lattice of 7\-topologies is both upper and lower semimodular. We also prove that the sublattice generated by the covers of a 7\-topology is isomorphic to the Boolean lattice of all subsets of the set of covers.
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تاریخ انتشار 2010