On continuity of homomorphisms between topological Clifford semigroups

I. Pastukhova

Abstract


Generalizing an old result of Bowman we prove that a homomorphism $f:X\to Y$ between topological Clifford semigroups is continuous if

  • the idempotent band $E_X=\{x\in X:xx=x\}$ of $X$ is a $V$-semilattice;
  • the topological Clifford semigroup $Y$ is ditopological;
  • the restriction $f|E_X$ is continuous;
  • for each subgroup $H\subset X$ the restriction $f|H$ is continuous.

Keywords


ditopological unosemigroup, Clifford semigroup, topological semilattice

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