Fuzzy Sets and Systems 133 (2003) 375–387 www.elsevier.com/locate/fss Generalized Lowen functors  Sanjiang Li a ; ∗ , Maokang Luo b a Department of Computer Science and Technology, State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China b Department of Mathematics, Sichuan University, Chengdu 610064, China Received 17 November 1999; received in revised form 4 June 2002; accepted 30 July 2002 Abstract According to their value ranges, L-topological spaces form dierent categories. Clearly, the investigation on their relationships is certainly important and necessary. Lowen was one of the rst authors who had studied the relation between the category of I -topological spaces and that of topological spaces. He introduced two well-known functors: ! and –. Later, these functors, namely Lowen functors, were extended by dierent authors for various kinds of lattices studying the relation between L-TOP and TOP. In this paper, we introduce two functors ! f and – f between L 1 -TOP and L 2 -TOP for each Scott continuous mapping f : L 2 → L 1 , where L 1 and L 2 are arbitrary two completely distributive lattices. Some topological properties related to these functors are revealed, e.g., for L i -topological space (X i ; i )(i =1; 2), both ! f (X 1 ; 1 ) and – f (X 2 ; 2 ) are Lowen spaces; in the case that f is the identity mapping on a linearly ordered complete lattice, for L-topological space (X;), ! f () is the nest Lowen topology on X contained in  and – f () is the coarsest Lowen topology on X containing , etc. c  2002 Elsevier Science B.V. All rights reserved. Keywords: Lowen space; Fuzzy topology; L-topological space; L-topology; (f-)Lowen functors; Completely distributive lattice; Scott continuous; (f-)induced space 0. Introduction Since the introduction of the fundamental concept of fuzzy sets given by Zadeh in 1965, usually, the value range used to express membership degrees in a certain investigation was a certain xed lattice. But as well known, in practical situations or procedures, value ranges in various systems used to estimate memberships are not necessary to be the same; meanwhile, the relationships among  Project supported by the National Natural Science Foundation of China, the Science Foundation of Education Ministry of China and the National Science Foundation for “Outstanding Young Scholars” of China. * Corresponding author. E-mail addresses: lisanjiang@tsinghua.edu.cn (S. Li), makaluo@scu.edu.cn (M. Luo). 0165-0114/02/$ - see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0165-0114(02)00384-6