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Semigroups of Isotone Selfmaps on Partially Ordered Sets
Author(s) -
Thornton M. C.
Publication year - 1976
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-14.3.545
Subject(s) - mathematics , semigroup , homomorphism , converse , automorphism , pure mathematics , order (exchange) , class (philosophy) , characterization (materials science) , semilattice , algebraic number , algebraic structure , algebra over a field , discrete mathematics , mathematical analysis , computer science , physics , geometry , finance , artificial intelligence , optics , economics
The continuous functions from X into itself form a semigroup S(X) . A class of spaces is considered so that S(X) is also the semigroup of isotone functions for a partial order on X . For this class, necessary and sufficient conditions are given for a semigroup to be isomorphic to some S(X) . The homomorphisms among these semigroups are studied and both the isomorphisms and the automorphisms are determined. For finite X , a converse to a theorem of Howie is proved, providing a characterization of X being totally ordered in terms of the algebraic structure of S(X) .