Gδ-separation axioms in ordered fuzzy topological spaces

The fuzzy concept has invaded all branches of Mathematics ever since the introduction of fuzzy set by Zadeh [10]. Fuzzy sets have applications in many fields such as information [5] and control [8]. The theory of fuzzy topological spaces was introduced and developed by Chang [3] and since then various notions in classical topology have been extended to fuzzy topological spaces. Sostak [6] introduced the fuzzy topology as an extension of Chang’s fuzzy topology. It has been developed in many directions. Sostak [7] also published a new survey article of the developed areas of fuzzy topological spaces. Katsaras [4] introduced and studied ordered fuzzy topological spaces. Motivated by the concepts of fuzzy Gδ-set [2] and ordered fuzzy topological spaces the concept of increasing (decreasing) fuzzy Gδ-sets, fuzzy Gδ–T1 ordered spaces and fuzzy Gδ–T2 ordered spaces are studied. In this paper we introduce some new separation axioms in the ordered fuzzy topological spaces and we establish an analogue of Urysohn’s lemma.