On nominal sets with support-preorder

Document Type : Research Paper


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.


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.


Main Subjects

[1] Amorim, A.A., Binding Operators for Nominal Sets, Electron. Notes Theor. Comput. Sci. 325 (2016), 3-27.
[2] Bojańczyk, M., Klin, B., and Lasota, S., Automata Theory in Nominal Sets, Log. Methods Comput. Sci. 10(3:4) (2014), 1–44.
[3] Fraenkel, J.A., Der begriff definit und die unabhangigkeit des auswahlsaxioms, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse (1922), 253-257.
[4] Fernandez, M., Gabbay, M.J., Nominal rewriting, Inform. and Comput. 205(6) (2007), 917-965.
[5] Gabbay, M.J., and Hofmann, M., Nomianl renaming sets, In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR (2008), 158-173, part of Lecture Notes in Comput. Sci. 5330, Springer.
[6] Gabbay, M.J. and Pitts, A.M., A new approach to abstract syntax with variable binding, Form. Asp. Comput. 13 (2002), 341-363.
[7] Munkres, J.R., “Topology", Prentice Hall, Incorporated, 2000.
[8] Pitts, A.M., “Nominal Sets: Names and Symmetry in Computer Science, Cambridge Tracts in Theoretical Computer Science", Cambridge University Press, 2013.