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A completion-invariant extension of the concept of meet continuous lattices

Published online by Cambridge University Press:  15 May 2015

WENFENG ZHANG  and
XIAOQUAN XU
WENFENG ZHANG
Affiliation:
School of Mathematics and Computer Science, Jiangxi Science & Technology Normal University, Nanchang 330038, China Email: zhangwenfeng2100@163.com
XIAOQUAN XU
Affiliation:
Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China Email: xiqxu2002@163.com
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Abstract

In this paper, the concept of meet F-continuous posets is introduced. The main results are: (1) A poset P is meet F-continuous iff its normal completion is a meet continuous lattice iff a certain system γ(P) which is, in the case of complete lattices, the lattice of all Scott closed sets is a complete Heyting algebra; (2) A poset P is precontinuous iff P is meet F-continuous and quasiprecontinuous; (3) The category of meet continuous lattices with complete homomorphisms is a full reflective subcategory of the category of meet F-continuous posets with cut-stable maps.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 4: Symposium on Domain Theory (ISDT 2013) , May 2017 , pp. 530 - 539
Copyright
Copyright © Cambridge University Press 2015 

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