Incomparable compactifications of the ray with Peano continuum as remainder

Bartoš, Adam; Marciňa, Radek; Pyrih, Pavel; Vejnar, Benjamín

doi:10.1016/j.topol.2016.05.008

Cited by 2 publications

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“…2 , and the claim follows since the mapπ 2 R ⊆ ∩K(X) 2 is closed by Lemma 4.12. If F is analytic, then H is analytic since K(X) is Polish and R ⊆ is closed in K(X)2 by Observation 4.11. The claim follows since the map π 2 is continuous.…”

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confidence: 80%

“…Original motivation comes from our interest in spirals [2] and from the construction of Minc [12], who for each nondegenerate metric continuum X constructed a metrizable compactum K whose components form a pairwise non-homeomorphic family of spirals over X with the decomposition space being 2 ω , and asked [12,Question 1] whether there is a metrizable compactum K whose set of components is equivalent to the class of all spirals over X, i.e. whether the class of all spirals over X is compactifiable.…”

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confidence: 99%

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Compactifiable classes of compacta

Bartoš

Bobok

Mill

et al. 2019

Topology and its Applications

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We introduce the notion of compactifiable classes -these are classes of metrizable compact spaces that can be up to homeomorphic copies "disjointly combined" into one metrizable compact space. This is witnessed by so-called compact composition of the class. Analogously, we consider Polishable classes and Polish compositions. The question of compactifiability or Polishability of a class is related to hyperspaces. Strongly compactifiable and strongly Polishable classes may be characterized by the existence of a corresponding family in the hyperspace of all metrizable compacta. We systematically study the introduced notions -we give several characterizations, consider preservation under various constructions, and raise several questions.Classification: 54D80, 54H05, 54B20, 54E45, 54F15.

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confidence: 80%