Topology and its Applications 158 (2011) 1192–1205 Contents lists available at ScienceDirect Topology and its Applications www.elsevier.com/locate/topol Induced maps on n-fold symmetric product suspensions Franco Barragán 1 Facultad de Ciencias Físico Matemáticas, BUAP, Ave. San Claudio y Rio Verde, Ciudad Universitaria, San Manuel Puebla, Pue. C.P. 72570, Mexico article info abstract Article history: Received 21 January 2010 Received in revised form 14 April 2011 Accepted 14 April 2011 MSC: 54B20 Keywords: Continuum Confluent map Monotone map Open map Quasi-interior map Symmetric product In a previous paper, we define the n-fold symmetric product suspensions of continua. Now, we investigate the induced maps between these spaces.  2011 Elsevier B.V. All rights reserved. 1. Introduction In 1979 Sam B. Nadler Jr. introduced the hyperspace suspension of a continuum [1]. In 2004 S. Macías, defined the n-fold hyperspace suspension of a continuum [2]. For a continuum X and n  2, in 2009, we define the n-fold symmetric product suspensions of X [3], denoted by SF n ( X ), as the quotient space F n ( X )/ F 1 ( X ), where F n ( X ) is the hyperspace of nonempty subsets of X with at most n points. Given a map f : X → Y between continua and an integer n  2, we let F n ( f ) : F n ( X ) → F n (Y ) and SF n ( f ) : SF n ( X ) → SF n (Y ) denote the corresponding induced maps. Let M be a class of maps between continua. As it was done with hyperspaces (see, for example [4–8]), in this paper we study the interrelations between the following three statements: (1) f ∈ M; (2) F n ( f ) ∈ M; (3) SF n ( f ) ∈ M. The paper consists of ten sections. In Section 2, we give the basic definitions for understanding the paper. In Section 3, we study homeomorphisms. Section 4 is devoted to monotone maps. Section 5 is about open maps. In Section 6, we discuss confluent maps. The light maps are analyzed in Section 7. In Section 8, we consider the class of quasi-interior maps and the class of MO-maps. In Section 9, we prove results concerning to the class of quasi-monotone maps and the class of weakly monotone maps. Finally, in Section 10 we study the class of weakly confluent maps and the class of pseudo-confluent maps. E-mail address: frabame@hotmail.com. 1 This research is part of the author’s Dissertation under the supervision of Professors Raúl Escobedo and Sergio Macías. 0166-8641/$ – see front matter  2011 Elsevier B.V. All rights reserved. doi:10.1016/j.topol.2011.04.006