J. Aust. Math. Soc.
73 (2002), 433445

Dense subsemigroups of generalised transformation semigroups

Amorn Wasanawichit
Department of Mathematics
Chulalongkorn University
Bangkok 10330
Thailand



Yupaporn Kemprasit
Department of Mathematics
Chulalongkorn University
Bangkok 10330
Thailand



Abstract

In 1986, Higgins proved that
, the semigroup (under composition) of all total
transformations of a set
, has a proper dense subsemigroup if and only if
is infinite, and he obtained similar results
for partial and partial onetoone
transformations. We consider the generalised
transformation semigroup
consisting of all total transformations from
into
under the operation
, where
is any fixed element
of . We show that this semigroup has a proper dense
subsemigroup if and only if
and
are infinite and
, and we
obtain similar results for partial and
partial onetoone transformations. The results
of Higgins then become special cases.

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