Convexity-preserving Properties of Partial Binary Operations with Respect to Filter Convex Structures on Effect Algebras

Wei, Xiaowei; Shi, Fu-Gui

doi:10.1007/s10773-022-05189-5

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2024

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“…Further, convexity also has a close relation with algebra. Wei and Shi [12,13] proved all filters on effect algebras form a convexity. Dong and Shi [2] introduced convex structures on MV-algebras such that the MV-operations are convexity-preserving or weak convexity-preserving.…”

Section: Introductionmentioning

confidence: 99%

The convexity induced by quasi-consistency and quasi-adjacency

Wang,

Shı

2024

Hacettepe Journal of Mathematics and Statistics

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In this paper, we introduce (quasi-)consistent spaces and (quasi-)adjacent spaces to characterize convexity spaces. Firstly, we show that convexity spaces can be characterized by quasi-consistent spaces. They can be induced by each other. In particular, each convexity space can be quasi-consistentizable. Every quasi-consistency U can induce two hull operators and thus determine different convexities CU and CU. And CU = CU holds when U is a consistency. Secondly, we use quasi-adjacent spaces to characterize convexity spaces. Each convexity space can be quasi-adjacentizable. In both of characterizations of convexity, remotehood systems play an important role in inducing convexity. Finally, we show there exists a close relation between a quasi-consistency and a quasi-adjacency. Furthermore, there exists a one-to-one correspondence between a quasi-adjacency and a fully ordered quasi-consistency. And we deeply study the relationships among these structures.

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Section: Introductionmentioning

confidence: 99%