Support Distance on Nominal Sets

In this paper, we introduce a distance-based structure on nominal sets by defining an equivariant support-distance derived from the symmetric difference of supports. This construction yields a natural notion of continuity for equivariant maps that reflects variations in support. Fixing a finitely supported family LCP(A) closed under finite unions and intersections, we associate to each nominal set an induced C-topology generated by support-distance balls. For support-surjective equivariant maps, we prove that distance-based continuity implies continuity with respect to the induced C-topology. As an application, we provide a topological characterization of To-support and T۲-support nominal spaces in terms of the separation by L-basic open balls.

کلیدواژه ها:

Nominal set ، support ، topology ، metric space