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SCIENCE CHINA Information Sciences, Volume 59, Issue 3: 032201(2016) https://doi.org/10.1007/s11432-015-5416-5

$L$-quantum spaces

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  • ReceivedMar 4, 2015
  • AcceptedJul 7, 2015
  • PublishedJan 22, 2016

Abstract

In this paper, based on a complete residuated lattice $L$, we introduce the definitions of $L$-quantum spaces and continuous mappings. Then we establish an adjunction between the category of stratified $L$-quantum spaces and the opposite category of two-sided $L$-quantales. We also prove that the category of sober $L$-quantum spaces is dually equivalent to the category of spatial two-sided $L$-quantales.


Funded by

the National Natural Science Foundation of China(11301316)

the National Natural Science Foundation of China(11531009)

Fundamental Research Funds for the Central Universities(GK201501001)


Acknowledgment

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11531009, 11301316) and the Fundamental Research Funds for the Central Universities (Grant Nos. GK201501001).


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