Subsets of compacta

Michael Laidacker

Displaying similar documents to “Subsets of compacta”

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...

Whitney properties

J. Krasinkiewicz, Sam Nadler (1978)

Fundamenta Mathematicae

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On pointed 1-movability and related notions

J. Krasinkiewicz (1981)

Fundamenta Mathematicae

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On the hyperspaces of snake-like and circle-like continua

J. Krasinkiewicz (1974)

Fundamenta Mathematicae

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Continua which cannot be mapped onto any nonplaner circle-like continuum

George W. Henderson (1971)

Colloquium Mathematicae

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On Cosserat continua

S. Drobot (1971)

Applicationes Mathematicae

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Cantor's Continuum Hypothesis: consequences in mathematics and its foundations

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.

Limiting subcontinua and Whitney maps of tree-like continua

Hisao Kato (1988)

Compositio Mathematica

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Chainable continua and homeomorphisms of the plane onto itself

Mirosław Sobolewski (1984)

Fundamenta Mathematicae

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Expansive collections of continua

Donald E. Bennett (1978)

Commentationes Mathematicae Universitatis Carolinae

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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.