LG-FUZZY PARTITION OF UNITY

  • Marzieh . Mostafavi Department of Mathematics, University of Qom, Qom, IRAN
Keywords: C∞ LGc-fuzzy topological manifold; LG-fuzzy exhaustion; LG-partitions of unity.

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.
Published
2022-12-30