Transfer closed and transfer open multimaps in minimal spaces M. Alimohammady * , M. Roohi, M.R. Delavar Department of Mathematics, University of Mazandaran, Babolsar 47416-1468, Iran Accepted 29 August 2007 Abstract This paper is devoted to introduce the concepts of transfer closed and transfer open multimaps in minimal spaces. Also, some characterizations of them are considered. Further, the notion of minimal local intersection property will be introduced and characterized. Moreover, some maximal element theorems via minimal transfer closed multimaps and minimal local intersection property are given. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction and preliminaries It is well known that topological concepts have many applications in modern physics. For example, the topology of quantum spacetime is shadowed closely by the Mobius geometry of quasi-Fuschian and Kleinian groups and that is the cause behind the phenomena of high-energy particle physics [11]. In fact, considering the spacetime as the product of two topologies, the topology of space and that of the spacetime will open the way for new line of research in the field of quantum gravity initiated by Witten and El-Naschie. For the relation between Wild Topology, Hyperbolic Geometry and Fusion Algebra with Coupling constants of the standard model and quantum gravity and close connection between e 1 theory and the topological theory of four manifolds, we refer to [12,13] and for the relation between topological concepts and geometrical properties of the e 1 spacetime to [14]. For another example, constructing a topology via a relation on a real-life data will help in mathematizing many fields. In fact, if X is a collection of symptoms and diseases in a certain region and R is a binary relation on X given by an expert the topology on X generated by R is a knowledge base for X, indication of symptoms for a fixed disease can be seen through the topology [7]. Since topology has very important applications in applied sciences, so studying of minimal structure as a general- ization of topology is important from this point of view. Minimal structures may have very important applications in quantum particles physics, particularly in connection with string theory and e 1 theory [6,8–10]. The work presented 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.08.071 * Corresponding author. E-mail addresses: amohsen@umz.ac.ir (M. Alimohammady), m.roohi@umz.ac.ir (M. Roohi), m.rostamian@umz.ac.ir (M.R. Delavar). Chaos, Solitons and Fractals 40 (2009) 1162–1168 www.elsevier.com/locate/chaos