Generating the full transformation semigroup using order preserving mappings

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18 Citations (Scopus)


For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappings O-X on X modulo the full transformation semigroup Ex. In other words, we ask what is the smallest cardinality of a set A of mappings such that <O-X boolean OR A> = T-X. When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set of real numbers) it is uncountable.

Original languageEnglish
Pages (from-to)557-566
Number of pages10
JournalGlasgow Mathematical Journal
Issue number3
Publication statusPublished - Sept 2003


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