Making Holes in the Hyperspace of Subcontinua of Some Continua

Anaya, José G.; Castañeda-Alvarado, Enrique; Orozco-Zitli, Fernando

doi:10.4236/apm.2012.22020

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…El primero es el estudio de los agujeros en el hiperespacio suspensión H(X) = C(X)/F 1 (X), ver [6]. El segundo aborda este problema para C(X) de dendroides suaves, ver [3]. La existencia de otras clases de continuos y de otros tipos de hiperespacios, abre una gran gama de posibles objetos de estudio.…”

Section: Conclusionesunclassified

Reseña de la búsqueda de hacer agujeros

Anaya

Maya

2018

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Resumen. Un espacio topológico conexo Z es unicoherente si para cualesquiera A y B cerrados y conexos de Z, tales que Z = A ∪ B, se tiene que A ∩ B es conexa. Sea Z un espacio unicoherente: decimos que z ∈ Z agujera a Z si Z − {z} no es unicoherente. Un problema de reciente estudio es: dado un espacio topológico unicoherente H(Z), obtenido de un espacio topológico Z, ¿cuáles elementos A ∈ H(Z) lo agujerean? Este trabajo consiste en dar una reseña de los resultados que hasta la fecha se conocen de este problema. Palabras clave: Continuo, hiperespacios, propiedad b), unicoherencia, cono, suspensión. MSC2010: 54B15, 54B20, 54F55.Abstract. A connected topological space Z is unicoherent provided that if Z = A ∪ B, where A and B are closed connected subsets of Z, then A ∩ B is connected. Let Z be a unicoherent space: we say that z ∈ Z makes a hole in Z if Z − {z} is not unicoherent. A problem of recent study is: given a topological space unicoherent H(Z), obtained from a topological space Z, which elements A ∈ H(Z) makes a hole? This work consists in giving a review of the results known to date of this problem.Iniciemos con el siguiente concepto, que es una herramienta muy útil en la búsqueda de agujeros. Sea Z un espacio topológico. Decimos que Z tiene la propiedad b) si para cada

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Section: Conclusionesunclassified

Reseña de la búsqueda de hacer agujeros

Anaya

Maya

2018

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“…So it becomes interesting to determine the elements that make a hole in these hyperspaces. In this direction, see [1], [2] and [4], for what is known about this problem. This section is dedicated to giving an application in hyperspaces of what we have developed.…”

Section: Making Holes In Hyperspacesmentioning

confidence: 99%

Making holes in the cone, suspension and hyperspaces of some continua

Anaya¹,

Castañeda-Alvarado²,

de³

et al. 2018

Commentationes Mathematicae Universitatis Carolinae

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“…Readers specially interested in this problem are refered to Anaya (2007Anaya ( , 2011, Orozco-Zitli (2010, 2012).…”

Section: Introductionmentioning

confidence: 99%

Making Holes in the Second Symmetric Product of a Cyclicly Connected Graph

Anaya¹,

Maya²,

Orozco-Zitli³

2014

JMR

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A continuum is a connected compact metric space. The second symmetric product of a continuum X, F 2 (X), is the hyperspace of all nonempty subsets of X having at most two elements. An element A of F 2 (X) is said to make a hole with respect to multicoherence degree in F 2 (X) if the multicoherence degree of F 2 (X) − {A} is greater than the multicoherence degree of F 2 (X). In this paper, we characterize those elements A ∈ F 2 (X) such that A makes a hole with respect to multicoherence degree in F 2 (X) when X is a cyclicly connected graph.

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Making Holes in the Hyperspace of Subcontinua of Some Continua

Cited by 6 publications

References 5 publications

Reseña de la búsqueda de hacer agujeros

Reseña de la búsqueda de hacer agujeros

Making holes in the cone, suspension and hyperspaces of some continua

Making Holes in the Second Symmetric Product of a Cyclicly Connected Graph

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