论文标题
数字拓扑组
Digital topological groups
论文作者
论文摘要
在本文中，我们发展了数字拓扑组的基本理论。基本定义基于组乘法所需的连续性的详细信息直接导致两个单独的类别。我们定义$ \ np_1 $ - 和$ \ np_2 $ - 数字拓扑组，并研究其属性和代数结构。 $ \ np_2 $类别非常限制，我们将提供$ \ np_2 $ - 数字拓扑组的完整分类。我们还提供了许多$ \ np_1 $ - 数字拓扑组的示例。我们定义数字拓扑组同态，并描述第一个同构定理的数字对应物。
In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate categories, based on the details of the continuity required of the group multiplication. We define $\NP_1$- and $\NP_2$-digital topological groups, and investigate their properties and algebraic structure. The $\NP_2$ category is very restrictive, and we give a complete classification of $\NP_2$-digital topological groups. We also give many examples of $\NP_1$-digital topological groups. We define digital topological group homomorphisms, and describe the digital counterpart of the first isomorphism theorem.
