Abstract. Let X be a continuum. For any positive integer n we consider the hyperspace Fn(X) and if n is greater than or equal to two, we consider the quotient space SF n(X ) defined in [3]. For a given map f : X → X, we consider the induced maps Fn(f ) : Fn(X) → Fn(X) and SFn(f ) : SF n(X ) → SF n(X ) defined in [4]. Let M be one of the following classes of maps: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, minimal, irreducible, feebly open and turbulent. In this paper we study the relationships between the following statements: f ∈ M, Fn(f ) ∈ M and SF n(f ) ∈ M.
In 1979 Sam B. Nadler, Jr. defined the hyperspace suspension of a continuum. We define the n-fold symmetric product suspensions of a continuum using n-fold symmetric products. We study some properties of this hyperspace: unicoherence, local connectedness, arcwise connectedness.
Abstract. We continue the work initiated by the first named author in Induced maps on n-fold symmetric product suspensions, Topology Appl. 158 (2011), 1192-1205. We consider classes of maps not included in the mentioned paper, namely: almost monotone, atriodic, freely decomposable, joining, monotonically refinable, refinable, semi-confluent, semi-open, simple and strongly freely decomposable maps.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.