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中文摘要：
引入Quantale系统的概念,给出了Quantale系统的连续映射和同胚映射的定义,证明了同胚映射的逆仍为同胚映射.探讨Quantale系统的空间化和Q-Locale化,并在Quantale系统范畴和量子空间范畴之间建立伴随.证明了Quantale系统关于Quantale的Q-Locale是Quantale系统,Quantale系统的Q-Locale化是Q-Locale.建立了Quantale系统范畴和Q-Loc范畴之间的伴随.
英文摘要：
By introducing the concept of Quantale system, the continuous mapping and homeomorphism of Quantale systems are defined. It is proved that the inverse of a homeomorphism mapping is also a homeomorphism mapping. Then the spatialization and the Q-localifieation of a Quantale system are researched and the adjoint between the category of Quantale system and the category of quantum spaces is established. It is proved the Q-loealification of a Quantale system and proved about Quantales is a Quantale system and the Q-localifieation of a Quantale system is Q-Locale. In the end, the adjoint between the category of Quantale systems and the category of Q-Loc is established.
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