拓扑效应代数

doi:10.6040/j.issn.1671-9352.0.2016.405

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 97-103.doi: 10.6040/j.issn.1671-9352.0.2016.405

拓扑效应代数

张巧卫¹,郭志华²,曹怀信²

1.榆林学院数学与统计学院, 陕西榆林 719000;2.陕西师范大学数学与信息科学学院, 陕西西安 710119

收稿日期:2016-09-02 出版日期:2017-10-20 发布日期:2017-10-12
作者简介:张巧卫(1983— ),女,副教授, 研究方向为量子信息与算子代数. E-mail:zhangqiaowei1188@sohu.com
基金资助:
国家自然科学基金资助项目(11501496);陕西省自然科学基础研究计划项目(2014JQ2-1003)

Topological effect algebras

ZHANG Qiao-wei¹, GUO Zhi-hua², CAO Huai-xin²

1. Department of Mathematics and Statistics, Yulin University, Yulin 719000, Shaanxi, China;
2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China

Received:2016-09-02 Online:2017-10-20 Published:2017-10-12

摘要/Abstract

摘要： 在一些经典效应代数上引入了拓扑结构,使其成为拓扑效应代数,证明了两个拓扑效应代数的直和仍是拓扑效应代数, 拓扑效应代数的模糊集系统仍是拓扑效应代数。给出了拓扑效应代数上连续映射的定义, 并研究了拓扑效应代数上态射(单调态射、同构)的连续性, 证明了从一个拓扑效应代数到另一个拓扑效应代数的全体连续映射之集仍是拓扑效应代数。

关键词: 拓扑效应代数, 连续映射, 态射

Abstract: Topological structure is introduced on some classic effect algebras, and so the effect algebras become topological effect algebras. We prove that the direct sum of two topological effect algebras is still topological effect algebra, and the fuzzy system of topological effect algebra is still topological effect algebra. Continious map between topological effect algebras are given, and the continuity of morphisms, monomorphisms and isomorphic are discussed. Finally, it is proved that the set of all continious maps from a topological effect algebra to another is also a topological effect algebra.

Key words: topological effect algebras, morphism, continuous map

中图分类号:

O177.1

张巧卫,郭志华,曹怀信. 拓扑效应代数[J]. 山东大学学报（理学版）, 2017, 52(10): 97-103.

ZHANG Qiao-wei, GUO Zhi-hua, CAO Huai-xin. Topological effect algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 97-103.

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拓扑效应代数

Topological effect algebras

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