L-quantum spaces

L-量子空间

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.

摘要

创新点

  1. (1)

    本文将量化的思想应用于量子空间, 提出了L-量子空间概念, 它可以看作是非交换的L-拓扑空间。

  2. (2)

    给出了L-量子空间上连续映射的概念, 探讨了它的一些性质。

  3. (3)

    研究了L-量子空间的一些范畴性质, 比如 : L-量子空间范畴可以与双侧L-quantale范畴之间建立伴随。

  4. (4)

    得到了Sober L-量子空间范畴的一个等价范畴, 即空间式的双侧L-quantale范畴。

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Correspondence to Bin Zhao.

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Zhao, B., Ma, N. L-quantum spaces. Sci. China Inf. Sci. 59, 32201 (2016). https://doi.org/10.1007/s11432-015-5416-5

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Keywords

  • L-quantum space
  • L-quantale
  • adjunction
  • stratified L-quantum space
  • spatial two-sided L-quantale

关键词

  • L-量子空间
  • L-quantale
  • 伴随
  • 满层L-量子空间
  • 空间式双侧 L-quantale