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 a...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.展开更多
基金Supported by the National Natural Science Foundation of ChinaScience Foundation of the State Education Commision of China+1 种基金supported by the Fund for Excellent Young University Teachers of the State Educational Commission of Chinathe Ex-Oversea-
文摘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.
