Kovalevsky has developed an abstract cellular complex for representing digital images in the combinatorial grid. This paper initiates the notions of cellular homotopy and cellular path homotopy through the continuous connected preserving map and investigates some of their basic properties in the abstract cellular complex. Further, the concept of fundamental groups in the abstract cellular complex is introduced using the notion of cellular homotopy and some of their basic properties are investigated. Finally, the paper presents the concept of homology and fixed point property in the connected abstract cellular complex.

中文翻译：

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抽象元胞复合体中的代数不变量

科瓦列夫斯基开发了一种抽象的细胞复合体，用于在组合网格中表示数字图像。这篇论文通过连续连通的保留映射启动了细胞同伦和细胞路径同伦的概念，并研究了它们在抽象细胞复合体中的一些基本性质。此外，使用细胞同伦的概念引入了抽象细胞复合体中基本群的概念，并研究了它们的一些基本性质。最后，本文提出了连通抽象细胞复合体中同源性和不动点性质的概念。