有限数字单纯复形的数字Lusternik-Schnirelmann范畴
Digital Lusternik-Schnirelmann Category of Finite Digital Simplicial Complexes
何震 1杨子康 1王玉玉1
作者信息
摘要
给出有限数字单纯映射间的数字连续关系、数字连续类、有限数字单纯复形以及有限数字单纯映射的强数字等价等概念.在此基础上,定义了有限数字单纯复形的数字Lusternik-Schnirelmann范畴和数字几何Lus-ternik-Schnirelmann范畴.最后,给出了在强数字等价和强数字收缩的情况下,以上两个数字范畴的一些相关结论.
Abstract
In this paper,the concepts of the digital continuous relation,the digital contiguity class,the finite digital simpli-cial complex and the strong digital equivalence of finite digital simplicial mappings are given.Based on this,the digital Lus-ternik-Schnirelmann category and the digital geometric Lusternik-Schnirelmann category of finite digital simplicial com-plexes are defined.Finally,some conclusions are given about the above two digital categories in the case of strong digital equivalence and strong digital collapse.
关键词
有限数字单纯复形/数字Lusternik-Schnirelmann范畴/数字连续类/强数字等价/强数字收缩Key words
finite digital simplicial complexes/digital Lusternik-Schnirelmann category/digital contiguity class/strong digital equivalence/strong digital collapse引用本文复制引用
基金项目
国家自然科学基金(11301386)
天津市自然科学基金项目(19JCYBJC30300)
天津师范大学研究生创新项目(2022KYCX107Y)
出版年
2024
NETL
NSTL
万方数据