Induced mappings between quotient spaces of symmetric products of continua

Castañeda-Alvarado, Enrique; Orozco-Zitli, Fernando; Sánchez–Martínez, Javier

doi:10.1016/j.topol.2013.10.007

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…Given two integers n and m such that n > m ≥ 1, SF n m (X) denotes the quotient space F n (X)/F m (X) obtained by shrinking F m (X) to a point in F n (X), with the quotient topology [15]. Here, we denote the quotient map by q m : F n (X) → SF n m (X) and q m (F m (X)) by F m X .…”

Section: Preliminariesmentioning

confidence: 99%

“…Let n and m be two integers such that n > m ≥ 1 and let X be a continuum. Note that the function F n (f ) induces another map on the space SF n m (X) which is denoted by SF n m (f ) : SF n m (X) → SF n m (X) [15]. In this paper, we introduce the dynamical system (SF n m (X), SF n m (f )) and we investigate some relationships between the dynamical systems (X, f ), (F n (X), F n (f )), (SF n (X), SF n (f )) and (SF n m (X), SF n m (f )) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic properties of the dynamical system SFnm(X), SFnm(f))

2020

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Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic properties of the dynamical system SFnm(X), SFnm(f))

2020

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“…Readers especially interested in this topic are referred, for example, to [5], [7], [8], [11], [12], [16], [17]. Regarding induced mappings in quotient hyperspaces we refer the reader, for example, to [1], [3], [4], [6], [10], [30].…”

Section: Introductionmentioning

confidence: 99%

Induced mappings on $C_n(X)/{C_n}_K(X)$

2021

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Given a continuum $X$ and $n\in\mathbb{N}$. Let $C_n(X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components. Let ${C_n}_K(X)$ be the hyperspace of all elements in $C_n(X)$ containing $K$ where $K$ is a compact subset of $X$. $C^n_K(X)$ denotes the quotient space $C_n(X)/{C_n}_K(X)$. Given a mapping $f:X\to Y$ between continua, let $C_n(f):C_n(X)\to C_n(Y)$ be the induced mapping by $f$, defined by $C_n(f)(A)=f(A)$. We denote the natural induced mapping between $C^n_K(X)$ and $C^n_{f(K)}(Y)$ by $C^n_K(f)$. In this paper, we study relationships among the mappings $f$, $C_n(f)$ and $C^n_K(f)$ for the following classes of mappings: almost monotone, atriodic, confluent, joining, light, monotone, open, OM, pseudo-confluent, quasi-monotone, semi-confluent, strongly freely decomposable, weakly confluent, and weakly monotone.

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