Generating the Full Transformation Semigroup Using Order Preserving Mappings
نویسنده
چکیده
For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappingsOX on X modulo the full transformation semigroup TX . In other words, we ask what is the smallest cardinality of a set A of mappings such that 〈OX ∪A 〉 = TX . 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. 1991 Mathematics Subject Classification. 20M20, 06A05.
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