# On nominal sets with support-preorder

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

2 Department of Mathematics, Velayat University, Iranshahr, Sistan and Balouchistan, Iran.

Abstract

Each nominal set 𝑋 can be equipped with a preorder relation ⪯ defined by the notion of support, so-called support-preorder. This preorder also leads us to the support topology on each nominal set. We study support-preordered nominal sets and some of their categorical properties in this paper. We also examine the topological properties of support topology, in particular separation axioms.

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