On the hyperspace suspension of a continuum

Escobedo, Raúl; López, María de J.; Macı́as, Sergio

doi:10.1016/j.topol.2003.08.024

Cited by 19 publications

(10 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1979 S. B. Nadler Jr., see [28], began the study of the quotient space C 1 (X)/F 1 (X), which he called the hyperspace suspension of X. Later, in 2004, R. Escobedo, M. de J. López and S. Macías extended the study of hyperspace suspension in [14].…”

Section: Introductionmentioning

confidence: 99%

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

2021

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

2021

View full text Add to dashboard Cite

show abstract

“…, where q X denotes the cannonical projection from C (X ) to HS (X ) [5]. That HS (f ) is continuous follows from [4, 4.3, p. 146].…”

Section: Introductionmentioning

confidence: 99%

Lifting Dynamical Properties to Hyperspaces

Masood

Singh

2014

Appl.Gen.Topol.

View full text Add to dashboard Cite

show abstract

“…The notion is a natural analogue of de Groot's concepts of absolute suspensions and absolute cones [3]. The continua that are absolute n-fold hyperspaces and the continua that are absolute hyperspaces of compacta were determined in [17].The notion of the hyperspace suspension of a continuum was introduced in 1979 [15] and studied further in [2]. The notion was extended to n-fold hyperspace suspensions in [12].…”

mentioning

confidence: 99%

“…The notion of the hyperspace suspension of a continuum was introduced in 1979 [15] and studied further in [2]. The notion was extended to n-fold hyperspace suspensions in [12].…”

mentioning

confidence: 99%

Absolute n-fold hyperspace suspensions

Macı́as¹,

Nadler

2006

Colloq. Math.

Self Cite

View full text Add to dashboard Cite

Abstract. The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finitedimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace suspensions must be unicoherent Hilbert cube manifolds.1. Introduction. The notion of an absolute hyperspace was introduced recently [17]. The notion is a natural analogue of de Groot's concepts of absolute suspensions and absolute cones [3]. The continua that are absolute n-fold hyperspaces and the continua that are absolute hyperspaces of compacta were determined in [17].The notion of the hyperspace suspension of a continuum was introduced in 1979 [15] and studied further in [2]. The notion was extended to n-fold hyperspace suspensions in [12].Our purpose here is to study absolute hyperspaces for the case of n-fold hyperspace suspensions. Our main results are Theorem 3.6, Theorem 3.7, Theorem 4.2, Corollary 4.4 and Theorem 4.9 in the finite-dimensional case, and Theorem 5.2 in the infinite-dimensional case. Our other results, such as Theorems 4.6 and 4.8, are used in the proofs of our main results and are also of independent interest.

show abstract

On the hyperspace suspension of a continuum

Cited by 19 publications

References 14 publications

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

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

Lifting Dynamical Properties to Hyperspaces

Absolute n-fold hyperspace suspensions

Contact Info

Product

Resources

About