标题： 代数拓扑中没有开集：极限空间中同伦理论的网络方法 显示英文标题

标题： Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces

摘要： 收敛空间是拓扑空间的推广。 收敛空间的范畴非常适合代数拓扑，其中一个原因是连续收敛提供了指数对象。 在本工作中，我们使用网理论的方法来研究收敛空间。 目标是简化连续收敛的描述，并将其应用于与同伦理论相关的问题。 我们提出了在极限空间中发展同伦理论基础的方法，定义基本群胚，并证明极限空间的Seifert-van Kampen定理的群胚版本。 显示英文摘要

摘要： Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this work, we use a net-theoretic approach to convergence spaces. The goal is to simplify the description of continuous convergence and apply it to problems related to homotopy theory. We present methods to develop the basis of homotopy theory in limit spaces, define the fundamental groupoid, and prove the groupoid version of the Seifert-van Kampen Theorem for limit spaces.