Now showing items 1-12 of 12

    • Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones 

      Elliott, L.; Jonusas, Julius; Mitchell, James D.; Morayne, Michal; Mesyan, Zak; Peresse, Yann (2023-08-22)
      In this paper we explore the extent to which the algebraic structure of a monoid M determines the topologies on M that are compatible withits multiplication. Specifically we study the notions of automatic continuity;minimal ...
    • The Bergman-Shelah Preorder on Transformation Semigroups 

      Mesyan, Zak; Mitchell, James D.; Morayne, Michal; Peresse, Yann (2012-11-01)
      Let $\nat^\nat$ be the semigroup of all mappings on the natural numbers $\nat$, and let $U$ and $V$ be subsets of $\nat^\nat$. We write $U\preccurlyeq V$ if there exists a countable subset $C$ of $\nat^\nat$ such that $U$ ...
    • Chains of subsemigroups 

      Cameron, Peter J.; Gadouleau, Maximilien; Mitchell, James D.; Peresse, Yann (2017-06)
      We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations ...
    • Computing finite semigroups 

      East, James; Egri-Nagy, Attila; Mitchell, James D.; Peresse, Yann (2019-05-01)
      Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples ...
    • Generating countable sets of surjective functions 

      Mitchell, James D.; Peresse, Yann (2011)
      We prove that any countable set of surjective functions on an infinite set of cardinality ℵn with n∈N can be generated by at most n2/2+9n/2+7 surjective functions of the same set; and there exist n2/2+9n/2+7 surjective ...
    • Generating sequences of functions, 

      Mitchell, James D.; Peresse, Yann; Quick, Martyn (2006-07-18)
      We consider the problem of obtaining an arbitrary countable collection of functions with specific properties as a composition of finitely many functions with the same property. The functions investigated are continuous, ...
    • GENERATING THE INFINITE SYMMETRIC GROUP USING A CLOSED SUBGROUP AND THE LEAST NUMBER OF OTHER ELEMENTS 

      Mitchell, James D.; Morayne, Michal; Peresse, Yann (2010-09-21)
      Let S∞ denote the symmetric group on the natural numbers N. Then S∞ is a Polish group with the topology inherited from NN with the product topology and the discrete topology on N. Let d denote the least cardinality of a ...
    • Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances 

      Mitchell, James D.; Morayne, Michal; Peresse, Yann; Quick, Martyn (2010-09-01)
      Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals ...
    • Polish topologies on endomorphism monoids of relational structures 

      Elliott, Luke; Jonusas, Julius; Mitchell, James D.; Peresse, Yann; Pinsker, Michael (2023-10-15)
      In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid End(A) of a countable relational structure A. As applications, we show that the endomorphism ...
    • Relative ranks of Lipschitz mappings on countable discrete metric spaces 

      Cichon, J.; Mitchell, James D.; Morayne, Michal; Peresse, Yann (2011-02-15)
      Let X be a countable discrete metric space and let XX denote the family of all functions on X. In this article, we consider the problem of finding the least cardinality of a subset A of XX such that every element of XX is ...
    • Sets of universal sequences for the symmetric group and analogous semigroups 

      Peresse, Yann; Hyde, James; Mitchell, James D.; Jonusas, Julius (2020-01-28)
      A universal sequence for a group or semigroup S is a sequence of words w1,w2,… such that for any sequence s1,s2,…∈S, the equations wi=si, i∈N, can be solved simultaneously in S. For example, Galvin showed that the sequence ...
    • Topological transformation monoids 

      Mesyan, Zak; Mitchell, James D.; Peresse, Yann (arXiv, 2018-09-12)
      We investigate semigroup topologies on the full transformation monoid T(X) of an infinite set X. We show that the standard pointwise topology is the weakest Hausdorff semigroup topology on T(X), show that the pointwise ...