From Support Metrics to Closure Operators: A Topological Approach to Nominal Sets

We introduce and study a topology on nominal sets induced by a support closure operator, which arises naturally from the action of finitary permutations on a countable set of atoms. This topology is generated by support classes and is closely related to a metric defined via symmetric differences of supports. We characterize continuous maps between nominal sets in this topological setting, investigate compactness and Hausdorffness properties and analyze the interplay between equivariance, support closure and topological structure. Our results provide new insights into the algebraic and topological aspects of nominal sets, enriching their theory and potential applications in areas such as logic, computer science and algebraic structures with name-binding.

کلیدواژه ها:

Closure operator ، Equivariant subset ، Support ، Topology ، Nominal set