简单1维数字流形的积空间中数字复叠的笛卡尔积的Deck变换群  

Deck Transformation Group of Cartesian Product of Digital Coverings in Product Space of Simple 1-dimensional Digital Manifolds

作　　者：张丛磊[1,3] 张志国 ZHANG Cong-lei;ZHANG Zhi-guo(College of Arts and Sciences,Shanxi Agricultural University,Jinzhong 030801,China;College of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030000,China;School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]山西农业大学文理学院,山西晋中030801 [2]山西师范大学数学与计算机科学学院,山西太原030000 [3]河北师范大学数学科学学院,河北石家庄050024

出　　处：《数学的实践与认识》2022年第2期181-187,共7页Mathematics in Practice and Theory

摘　　要：首先提出了简单1维数字流形的概念,接着研究了简单1维数字流形的具有C-相容邻接关系的笛卡尔积空间中的数字图像.进一步,为了研究数字复叠的笛卡尔积的Deck变换群,利用半径2-(k_(i2),k_(i1))-局部同胚的性质来体现数字复叠的笛卡尔积的Deck变换群在从数字拓扑的角度来比较数字积空间时的优势.此外,通过强调C-相容的必要性修正了文献(Han S E.Comparison among digital fundamental groups and its applications[J].Information Sciences,2008,178(8):2091-2104)中的一个错误.利用本文的方法,可以从本质上区分数字积图像,从而使得数字图像的研究内容更加丰富.We firstly propose the notion of simple 1-dimensional digital manifold in this paper.Then we study digital images in Cartesian product space of simple 1-dimensional digital manifolds with the C-compatible adjacency relation.Furthermore,in order to study Deck transformation group of Cartesian product of digital coverings,the paper uses some properties of radius 2(k_(i2),k_(i1))-local homeomorphism and shows the merits of Deck transformation group of a Cartesian product of digital coverings in comparing digital products from the view point of digital topology.Moreover,we correct an error in(Han S E.Comparison among digital fundamental groups and its applications[J].Information Sciences,2008,178(8):2091-2104)by emphasizing the necessity for C-compatible.By this approach,we can substantially distinguish digital products images so that enrich the information of digital images.

关 键 词：简单1维数字流形 C-相容邻接 Deck变换群 半径2-(k_(i2) k_(i1))-局部同胚 (k k')-同伦等价 

分 类 号：O152[理学—数学]