Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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9 citations
TL;DR: For a semigroup S, the set of all subsemigroups of S × S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by bS as discussed by the authors.
9 citations
TL;DR: In this article, the authors introduce the notion of continuous lattices, a class of compact semilattices having enough homomorphisms into the unit interval semilatice.
Abstract: and what nowadays, in more general form, is called domains, whileJ. D. LAWSON drew semigroup theoreticians' attention to a very natural class of compact semilattices having enough homomorphisms into the unit interval semilattice. The class of continuous lattices agrees with the class of Lawson semilattices. It generates a network of applications in theoretical computer science under the name "domain theory". - A hundred years after SOPHUS LIE's differentiable groups and semigroups, attention returned back to semigroups and Lie theory. Lie semigroup theory, initiated by E. B. VINBERG, G. I. OLSHANSKY, J. D. LAWSON and the author among others, infused a strong geometric and analytical flavor into topological semigroup theory and generated a new lines of application of semigroup theory such as in geometric control theory, and in the area of unitary representation theory of Lie groups, particulary in the area of holomorphic extensions of unitary representations. A respectable number of mongraphs and collections have been and are being written in this field.
9 citations
TL;DR: The semigroup End(X, ⩽) of isotonic mappings of a linearly ordered set as well as the transition semigroups of automata that arise from certain varieties of formal languages are discussed.
9 citations
01 Jan 2007
9 citations