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Topology as Faithful Communication Through Relations
Fundamenta Informaticae ( IF 1.166 ) Pub Date : 2020-10-31 , DOI: 10.3233/fi-2020-1963
Samuele Maschio 1 , Giovanni Sambin 1
Affiliation  

Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the two sides of basic pairs. In particular, we prove that the subsets which can be communicated faithfully (in the suitable way) are exactly open subsets and closed subsets. We also prove that a relation (and in particular a function) between two sets of points can be communicated faithfully if and only if it is continuous.

中文翻译:

作为通过关系进行忠实通信的拓扑

基本对及其态射是可以定义标准拓扑概念的最基本框架。我们在这里提出了拓扑概念的新解释,因为这些概念可以在基本对的两侧之间忠实地传达。特别地,我们证明了可以忠实地(以合适的方式)通信的子集是完全开放的子集和封闭的子集。我们还证明了两组点之间的关系(尤其是函数)可以忠实地传达当且仅当它是连续的。
更新日期:2020-10-31
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