一致分子格及其性质

Uniform molecular lattices and their properties

对分子格Ｌ上的自映射ｆ：Ｌ→Ｌ，提出了一种新的映射道ｆ－１：Ｌ→Ｌ，其中，对任意Ｌ中的元ａ，ｆ－１（ａ）＝∨｛ｂ∈Ｍ（Ｌ）｜ａ∧ｆ（ｂ）≠０｝．借助于此，引入了分子格上的一种对称的一致结构，证明了一个拓扑分子格（Ｌ，η）可一致化当且仅当它是全正则分子格．

For a mapping f: L→L over a molecular lattice L, a new mapping inverse f-1:L →L of f is introduced, which is defined by f-1(a) =V {b∈M(L)|a∧f(b)≠0} for every a ∈ L. Based on the concept of mapping inverse just introduced, a symmetric uniform structure over a molecular lattice is defined. And the following result is shown: a topological molecular lattice can be uniformlied if and only if it is a completely regular molecular lattice which is defined.