有限数字单纯复形的数字Lusternik-Schnirelmann范畴  

Digital Lusternik-Schnirelmann Category of Finite Digital Simplicial Complexes

作　　者：何震 杨子康 王玉玉 He Zhen;Yang Zikang;Wang Yuyu(Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学,天津300387

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期25-29,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：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)。

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LusternikSchnirelmann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。In this paper,the concepts of the digital continuous relation,the digital contiguity class,the finite digital simplicial complex and the strong digital equivalence of finite digital simplicial mappings are given.Based on this,the digital Lusternik-Schnirelmann category and the digital geometric Lusternik-Schnirelmann category of finite digital simplicial complexes 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 

分 类 号：O189.23[理学—数学]