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M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 2,  2011, pp.279-300
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.2.279
 Title & Authors
M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS
Yao, Wei;
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 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;
 Language
English
 Cited by
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