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(L, *)-valued coarse structures on powersets
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DOI：10.1016/j.fss.2023.108659.png)
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摘要
En 中文
The main purpose of this paper is to establish a fundamental framework of L-valued coarse structures. At first an approach to fuzzification of the notion of coarse structure is proposed. An L-valued coarse structure on a set Xas an L-fuzzy subset U of the powerset 2(XxX) satisfying L-valued analogues of the axioms of a coarse structure is given. Some basic properties of L-valued coarse structure spaces are studied. Then we introduce the notion of asymptotic dimension in [0, 1]-valued coarse spaces and show that the degree of asymptotic dimension is invariant under fuzzy coarse equivalences. (c) 2023 Elsevier B.V. All rights reserved.
Keyword:
Coarse structure
L-valued coarse structure
Fuzzy metric space
Fuzzy bornologous
Fuzzy coarse equivalence
Asymptotic dimension
期刊
IF:
2.7
论文数:
7.6K
被引数:
1.5W
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