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Essential and density topologies on s2-continuous posets

Published online by Cambridge University Press:  30 October 2017

CHONGXIA LU  and
QINGGUO LI
CHONGXIA LU
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China Emails: lcx19882016@aliyun.com, liqingguoli@aliyun.com
QINGGUO LI
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China Emails: lcx19882016@aliyun.com, liqingguoli@aliyun.com
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Abstract

Recently, Rusu and Ciobanu established that for a continuous domain L, a subset B of L is a basis if and only if B is dense with respect to the d-topology, called the density topology, on L. In situations where directed completeness fails, Erné has proposed in 1991 an alternative definition of continuity called s2-continuity which remedied the lack of stability of continuity under the classical Dedekind–MacNeille completion. In this paper, we show how the ‘Rusu–Ciobanu’ type of characterization can be formulated and established over the class of s2-continuous posets with appropriate modifications. Although we obtain more properties of essential topologies and density topologies on s2-continuous posets, respectively.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 10 , November 2018 , pp. 1770 - 1785
Copyright
Copyright © Cambridge University Press 2017 

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