A topological molecular lattice (TML) is a pair (L, r), where L is a completely distributive lattice and T is a subframe of L. There is an obvious forgetful functor from the category TML of TML’s to the category Loc ...A topological molecular lattice (TML) is a pair (L, r), where L is a completely distributive lattice and T is a subframe of L. There is an obvious forgetful functor from the category TML of TML’s to the category Loc of locales. In this note, it is showed that this forgetful functor has a right adjoint. Then, by this adjunction, a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.展开更多
In [6,11], A theory of pointwise pseudo-quasi-metrics was based on completely distributive lattices. In this paper a product pointwise p.q. metric function is constructed on the product of countably many molecular lat...In [6,11], A theory of pointwise pseudo-quasi-metrics was based on completely distributive lattices. In this paper a product pointwise p.q. metric function is constructed on the product of countably many molecular lattices by distance functions. Hence it is proved that countable product of pointwise pseudo-quasi-metric molecular lattices is pointwise pseudo-quasi-metrizable.展开更多
基金973 Programs (2002cb312200) Huo Yingdong Education Foundation and TRAPOYT.
文摘A topological molecular lattice (TML) is a pair (L, r), where L is a completely distributive lattice and T is a subframe of L. There is an obvious forgetful functor from the category TML of TML’s to the category Loc of locales. In this note, it is showed that this forgetful functor has a right adjoint. Then, by this adjunction, a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.
基金Supported by the National Natural Science Foundation of China (19971059)
文摘In [6,11], A theory of pointwise pseudo-quasi-metrics was based on completely distributive lattices. In this paper a product pointwise p.q. metric function is constructed on the product of countably many molecular lattices by distance functions. Hence it is proved that countable product of pointwise pseudo-quasi-metric molecular lattices is pointwise pseudo-quasi-metrizable.
