
doi: 10.1007/bf02265398
Summary: As one of main backgrounds of locale theory, topologies have close connections with locales. But locales have other backgrounds such as algebra, mathematical logic, etc. So there are many differences between locales and topologies. Spatiality is an important localic property to investigate the connections between locales and topologies. The \(T_D\) property is a special separation property which plays an important role in this kind of investigations. Just as it will be proved in this paper, the \(T_D\) property often appears as the lowest requirement for many topological spaces such that they can be described with localic properties and vice versa. In this paper, we show these special properties of the \(T_D\) axiom and investigate some other interesting and important problems of \(T_D\)-spatiality of locales.
Lower separation axioms (\(T_0\)--\(T_3\), etc.), Heyting algebras (lattice-theoretic aspects), localic properties, separation property
Lower separation axioms (\(T_0\)--\(T_3\), etc.), Heyting algebras (lattice-theoretic aspects), localic properties, separation property
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