# M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS

• Yao, Wei (Department of Mathematics, Hebei University of Science and Technology)
• Accepted : 2011.06.04
• Published : 2011.06.25
• 86 16

#### 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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