Generating the full transformation semigroup using order preserving mappings

PM Higgins; James David Mitchell; Nikola Ruskuc

doi:10.1017/S0017089503001460

Generating the full transformation semigroup using order preserving mappings

PM Higgins, James David Mitchell, Nikola Ruskuc

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	557-566
Number of pages	10
Journal	Glasgow Mathematical Journal
Volume	45
Issue number	3
DOIs	https://doi.org/10.1017/S0017089503001460
Publication status	Published - Sept 2003

Keywords

Ranks

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10.1017/S0017089503001460

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Generating the full transformation semigroup using order preserving mappings

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Keywords

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