Quantum spaces

被引：0
作者：
Wei He
Mao Kang Luo
机构：
[1] Nanjing Normal University,Department of Mathematics
[2] Sichuan University,Institute of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2010年 / 26卷
关键词：
quantale; quantum space; Zariski spectrum; 54A05; 54B35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a more general concept of quantum space is given by modifying the original concept defined by Borceux and Bossche. We show that a quantum space is a topological analogue of a quantale defined by Mulvey, and also a non-commutative generalization of the Zariski spectrum of a commutative ring. But quantum spaces are not good enough to have much of the properties of topological spaces, such as product spaces and quotient spaces.
引用
收藏
页码：1323 / 1330
页数：7
相关论文
共 12 条
[1]  
Borceux F.(1989)An essay on non-commutative topology Topology Appl. 31 203-223
[2]  
Bossche G. V. D.(1986)Quantales and their sheaves Order 3 61-87
[3]  
Borceux F.(1988)Constructing locales from quantales Math. Proc. Camb. Phil. Soc. 104 215-234
[4]  
Bossche G. V. D.(1986)Categorical structures enriched in a quantaloid: orders and ideals overa based quantaloid & Rend. Circ. Mat. Palermo 12 99-104
[5]  
Niefield S. B.(2005)Étale groupoids and their quantales Applied Categorical Structures 13 235-255
[6]  
Rosenthal K. I.(2007)Weakly topological representation of locales Adv. Math. 208 147-209
[7]  
Mulvey C. J.(2004)A constructive proof of the Gelfand-Kolmogorov theorem Acta Mathematica Sinica, Chinese Series 47 601-606
[8]  
Stubbe I.(2004)undefined Applied Categorical Structures 12 197-202
[9]  
Resenda P.(undefined)undefined undefined undefined undefined-undefined
[10]  
He W.(undefined)undefined undefined undefined undefined-undefined
12