On continuity of homomorphisms between topological Clifford semigroups

  • I. Pastukhova Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
Keywords: ditopological unosemigroup, Clifford semigroup, topological semilattice
Published online: 2014-07-15

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.
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