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http://dx.doi.org/10.5831/HMJ.2011.33.2.279

M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS  

Yao, Wei (Department of Mathematics, Hebei University of Science and Technology)
Publication Information
Honam Mathematical Journal / v.33, no.2, 2011 , pp. 279-300 More about this Journal
Abstract
For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.
Keywords
M-way below; M-continuous; M-Scott topology; M-Scott convergence;
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