LG-FUZZY PARTITION OF UNITY

Marzieh Mostafavi
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引用次数: 0

Abstract

In this paper, we define LGc-fuzzy Euclidean topological space with countable basis, which L denotes a complete distributive lattice and we show that each LGc-fuzzy open covering of this space can be refined to an LGc-fuzzy open covering that is locally finite. We introduce C∞ LG-fuzzy manifold (X, Tc), with countable basis of LG-fuzzy open sets which X is an L-fuzzy subset of a crisp set M and T : LMX → L, is an L-gradation of openness on X. We prove that for any LG-fuzzy topological manifold (X,T), there exists an LG-fuzzy exhaustion. We prove LG-Urysohn lemma and also existence of LG-partitions of unity on every LG-fuzzy topological manifold.
单位的Lg-fuzzy划分
本文定义了具有可数基的lgc -模糊欧氏拓扑空间,其中L表示完全分布格,并证明了该空间的每个lgc -模糊开覆盖都可以细化为局部有限的lgc -模糊开覆盖。我们引入了C∞lg -模糊流形(X, Tc),它具有lg -模糊开集的可数基,其中X是一个清晰集M和T的L-模糊子集:LMX→L是X上开度的L-阶积。我们证明了对于任何lg -模糊拓扑流形(X,T),存在一个lg -模糊耗尽。我们证明了在每一个fuzzy拓扑流形上,LG-Urysohn引理和lg -分区的存在性。
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