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

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Abstract

In this paper, we obtain that all filters and the empty set of every effect algebra could naturally form a convex structure, which is called a filter convex structure, and morphism (resp., monomorphism) between two effect algebras is convexity-preserving (resp., convex-to-convex) correspondingly constructed convexity spaces. Then we introduce the concept of nets (convergent nets) in convexity spaces that is compatible with convexity-preserving mappings and investigate some properties of convergent nets. Moreover, we prove that the partial subtraction − for the first position is convexity-preserving and the partial addition + is separately convexity-preserving with respect to filter convex structures by nets. Finally, we discuss convexity-preserving properties of the partial subtraction − for the first position and that the partial addition + is separately convexity-preserving in quotient (resp., finite product) of filter convex structures. For finite product, we also investigate the opposite direction for the partial subtraction.

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Acknowledgements

This work is supported by the Natural Science Foundation of China (11871097, 12071033, 11971448) and Beijing Institute of Technology Science and Technology Innovation Plan Cultivation Project (2021CX01030).

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  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 102488, China

    Xiaowei Wei & Fu-Gui Shi

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  1. Xiaowei Wei
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  2. Fu-Gui Shi
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Correspondence to Fu-Gui Shi.

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Wei, X., Shi, FG. Convexity-preserving Properties of Partial Binary Operations with Respect to Filter Convex Structures on Effect Algebras. Int J Theor Phys 61, 195 (2022). https://doi.org/10.1007/s10773-022-05189-5

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