D-continua, D⁎-continua, and Wilder continua

Espinoza, Benjamin; Matsuhashi, Eiichi

doi:10.1016/j.topol.2020.107393

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…Since every nondegenerate indecomposable continuum has uncountably many composants [13,Theorem 11.15], we can easily see that every nondegenerate D-continuum is decomposable. For other relationships between the classes of the above continua and other classes of continua, see [2,Figure 6].…”

Section: Introductionmentioning

confidence: 99%

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Some decomposable continua and Whitney levels of their hyperspaces

Matsuhashi¹,

Oshima²

2022

Preprint

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We introduce the new class of continua; D * * -continua. The classes of Wilder continua and D * -continua are strictly contained in the class of D * * -continua. Also, the class of D-continua is bigger than the class of D * *continua. Using D * * -continua, we give the negative answer to [2, Question 2]. Furthermore, we prove that being Wilder, being D, being D * and being D * * are Whitney properties.

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Section: Introductionmentioning

confidence: 99%

“…D-continua have some nice properties, see [1], [2], [8], [9], [10], and [11]. Furthermore, D-continua are related to continua introduced by Janiszewski [4].…”

Section: Introductionmentioning

confidence: 99%

Some decomposable continua and Whitney levels of their hyperspaces

Matsuhashi¹,

Oshima²

2022

Preprint

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“…It is known that every colocally connected continuum is aposyndetic [12,Remark 5.4.15]. As the consequence, colocal connectedness implies many properties of continua (see [3,Figure 6]. See also [2, p.239] for other properties derived from colocal connectedness).…”

Section: Introductionmentioning

confidence: 99%

Some theorems on colocally connected continua

Matsuhashi¹,

Oshima²

2022

Preprint

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On Wilder, Strongly Wilder, Continuumwise Wilder, D, $$D^*$$, and $$D^{**}$$ Continua

Camargo,

Macías

2024

Bull. Malays. Math. Sci. Soc.

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We study properties of Wilder, strongly Wilder, continuumwise Wilder, D, $$D^*$$ D ∗ , and $$D^{**}$$ D ∗ ∗ Hausdorff continua. We present an example of a colocally connected continuum that is not a $$D^*$$ D ∗ -continuum, answering a question by Espinoza and Matsuhashi. We give several positive answers to this question for unicoherent continua. We also present some equivalences for the class of homogeneous Hausdorff continua with the property of Kelley.

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D-continua, D⁎-continua, and Wilder continua

Cited by 7 publications

References 12 publications

Some decomposable continua and Whitney levels of their hyperspaces

Some decomposable continua and Whitney levels of their hyperspaces

Some theorems on colocally connected continua

On Wilder, Strongly Wilder, Continuumwise Wilder, D, $$D^*$$, and $$D^{**}$$ Continua

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