We propose a novel topological perspective on data languages recognizable by orbit-finite nominal monoids. For this purpose, we introduce pro-orbit-finite nominal topological spaces. Assuming globally bounded support sizes, they coincide with nominal Stone spaces and are shown to be dually equivalent to a subcategory of nominal boolean algebras. Recognizable data languages are characterized as topologically clopen sets of pro-orbit-finite words. In addition, we explore the expressive power of pro-orbit-finite equations by establishing a nominal version of Reiterman's pseudovariety theorem.

翻译：我们提出了一种关于轨有限名义幺半群可识别的数据语言的新型拓扑视角。为此，我们引入了pro-轨有限名义拓扑空间。在全局有界支撑大小的假设下，这些空间与名义Stone空间重合，并被证明与名义布尔代数的一个子范畴呈对偶等价关系。可识别的数据语言被刻画为pro-轨有限字的拓扑闭开集。此外，我们通过建立Reiterman伪簇定理的名义版本，探讨了pro-轨有限方程的表示能力。