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Displaying similar documents to “Cantor's Continuum Hypothesis: consequences in mathematics and its foundations”

Non-separating subcontinua of planar continua

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.

Induced open projections and C*-smoothness

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).

1/2-Homogeneous hyperspace suspensions

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.

On indecomposability and composants of chaotic continua

Hisao Kato (1996)

Fundamenta Mathematicae

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A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that d ( f n ( x ) , f n ( y ) ) > c . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that d i a m i f n ( A ) > c . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua...