East Asian Mathematical Journal Vol. 27 (2011), No. 3, pp. 373–380 ON L-FUZZY ω-BASICALLY DISCONNECTED SPACES M. Sudha, E. Roja, and M. K. Uma Abstract. In this paper L-fuzzy ω-closed and L-fuzzy ω-open sets are introduced. Also a new class of L-fuzzy topological space called L-fuzzy ω-basically disconnected space is introduced. Several characterizations and some interesting properties are also given. 1. Introduction The fuzzy concept has invaded almost all branches of Mathematics since the introduction of the concept by Zadeh[14]. Fuzzy sets have applications in many fields such as information [10] and control [11]. The theory of fuzzy topological spaces was introduced and developed by Chang [3] and since then various important notions in classical topology have been extended to fuzzy topological spaces. Rodabaugh [7] discussed normality and the L-fuzzy unit interval. He [8] also studied fuzzy addition in the L-fuzzy real line. Hoeche [6] studied the characterizations of L-topologies by L-valued neighbourhoods. An L-fuzzy normal spaces and Tietze extension theorem were discussed by Tomash Kubiak [13]. The concept of ω-open set was studied in [9]. The purpose of this paper is to introduce L-fuzzy ω-closed, L-fuzzy ω-open sets and a new class of L-fuzzy topological spaces called L-fuzzy ω-basically disconnected space. In this connection several characterizations and some interesting properties are also given. 2. Preliminaries Definition 2.1. ([1]) Let (X, T ) be a fuzzy topological space and λ be a fuzzy set in (X, T ). λ is called a fuzzy G δ -set if λ = ∞  i=1 λ i where each λ i ∈ T,i ∈ I . Received September 16, 2009; Accepted February 14, 2011. 2000 Mathematics Subject Classification. 54A40,03E72. Key words and phrases. L-fuzzy ω-closed set, L-fuzzy ω-open set, L-fuzzy ω-basically disconnected space, L-fuzzy ω ∗ -continuous map, L-fuzzy ω ∗ -irresolute, strong Fσ L-fuzzy ω ∗ -continuous map, lower (upper) L-fuzzy ω ∗ -continuous map. c 2011 The Youngnam Mathematical Society 373