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Pure Mathematics 2024
模糊Riesz空间中的模糊序基和模糊不交系统的性质
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Abstract:
本文主要讨论了在模糊Riesz空间中的模糊序基和模糊不交系统的基本性质。首先讨论了由可数集{vn:n=1,2,？}生成的模糊带中元素的刻画。其次讨论了若Archimedean Riesz空间中模糊序稠理想是模糊super序稠的，则不交系统具有的一些基本性质。最后给出了模糊Archimedean Riesz空间中模糊理想具有可数或有限的模糊序基的条件，给出了模糊Archimedean Riesz空间模糊序可分的条件。
This paper discusses the fundamental properties of fuzzy order bases and fuzzy disjoint systems in fuzzy Riesz spaces. Firstly, it examines the characterization of elements in fuzzy bands generated by countable set{vn:n=1,2,？}. Then, it discusses some basic properties of non-intersecting systems if fuzzy order-dense ideals are fuzzy superorder dense in Archimedean Riesz spaces. Finally, it gives conditions for fuzzy ideals to have countable or finite fuzzy order bases in fuzzy Archimedean Riesz spaces and conditions for fuzzy order separability in fuzzy Archimedean Riesz spaces.
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