The Existence of the Complete and Completely Distributive Lattices

数学季刊 ›› 1996, Vol. 11 ›› Issue (2): 80-81.

The Existence of the Complete and Completely Distributive Lattices

Department of Mathematics,Hebei University,Baoding,071002

收稿日期:1996-01-30 出版日期:1996-06-30 发布日期:2025-01-13

The Existence of the Complete and Completely Distributive Lattices

Department of Mathematics,Hebei University,Baoding,071002

Received:1996-01-30 Online:1996-06-30 Published:2025-01-13

摘要/Abstract

摘要： The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory.In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the infinte complete and completely distributive lattice which has finite dimension.A complete boolean lattice Bpossesses the smallest set of generating elements iff B is completely distributive.

关键词: , topological lattice, smallest set of generating elements, intrinsic topology

Abstract: The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory.In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the infinte complete and completely distributive lattice which has finite dimension.A complete boolean lattice Bpossesses the smallest set of generating elements iff B is completely distributive.

Key words: , topological lattice, smallest set of generating elements, intrinsic topology

中图分类号:

O153

白瑞蒲. The Existence of the Complete and Completely Distributive Lattices[J]. 数学季刊, 1996, 11(2): 80-81.

Bai Ruipu. The Existence of the Complete and Completely Distributive Lattices[J]. Chinese Quarterly Journal of Mathematics, 1996, 11(2): 80-81.

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The Existence of the Complete and Completely Distributive Lattices

The Existence of the Complete and Completely Distributive Lattices

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