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An axiomatic approach to bases and subbases in L-convex spaces and their applications

机译：L-凸空间中的基和子基的公理化方法及其应用

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摘要

Considering a continuous lattice L as the lattice background, an axiomatic approach to bases and subbases in the framework of L-convex spaces is provided. Firstly, the concepts of bases and subbases in L-convex spaces are introduced and then L-convexity base axioms and L-convexity subbase axioms are proposed by abstracting the properties of bases and subbases, respectively. Secondly, some applications of L-convexity base axioms and L-convexity subbase axioms are investigated. It is shown that L-convexity base axioms can be used to demonstrate some relationship between spatial structures with respect to L-convex structures and L-convexity subbase axioms can be applied to define the join space and the product space of L-convex spaces. (C) 2018 Elsevier B.V. All rights reserved.
机译：以连续晶格L为晶格背景，提出了一种在L凸空间框架内对基和子基的公理化方法。首先，介绍了L-凸空间中的基和子基的概念，然后通过抽象基和子基的性质，提出了L-凸基公理和L-凸基公理。其次，研究了L-凸基公理和L-凸基公理的一些应用。研究表明，L-凸基公理可用于证明空间结构相对于L-凸结构的某些关系，L-凸基公理可用于定义L-凸空间的连接空间和乘积空间。 （C）2018 Elsevier B.V.保留所有权利。

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