On the consistency of the generalized continuum hypothesis
L. Rieger
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L. Rieger
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Uri Abraham, Saharon Shelah (2001)
Fundamenta Mathematicae
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Assuming the continuum hypothesis there is an inseparable sequence of length ω₁ that contains no Lusin subsequence, while if Martin's Axiom and ¬ CH are assumed then every inseparable sequence (of length ω₁) is a union of countably many Lusin subsequences.
Alessandro Andretta (2018)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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We give an overview of the continuum hypothesis, of its impact on mathematics, and on the foundations of set theory.
Giorgio Venturi, Matteo Viale (2018)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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In this article we review the present situation in the foundations of set theory, discussing two programs meant to overcome the undecidability results, such as the independence of the continuum hypothesis; these programs are centered, respectively, on forcing axioms and Woodin's V = Ultimate-L conjecture. While doing so, we briefly introduce the key notions of set theory.
Jerzy Krzempek (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
D. Daniel, C. Islas, R. Leonel, E. D. Tymchatyn (2015)
Colloquium Mathematicae
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We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.
Włodzimierz J. Charatonik, Alejandro Illanes, Verónica Martínez-de-la-Vega (2013)
Colloquium Mathematicae
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We show that there exists a C*-smooth continuum X such that for every continuum Y the induced map C(f) is not open, where f: X × Y → X is the projection. This answers a question of Charatonik (2000).
Roman Mańka (1987)
Colloquium Mathematicae
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Davis, H.S., Stadtlander, D.P., Swingle, P.M. (1962)
Portugaliae mathematica
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Donald E. Bennett (1978)
Commentationes Mathematicae Universitatis Carolinae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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T. Maćkowiak (1977)
Fundamenta Mathematicae
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Janusz Charatonik (1964)
Fundamenta Mathematicae
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Sergio Macías, Patricia Pellicer-Covarrubias (2012)
Colloquium Mathematicae
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We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.
Charatonik, Janusz J., Pyrih, Pavel (2000)
Mathematica Pannonica
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George W. Henderson (1971)
Colloquium Mathematicae
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Roman Mańka (2002)
Fundamenta Mathematicae
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It is proved that the cylinder X × I over a λ-dendroid X has the fixed point property. The proof uses results of [9] and [10].