Connexions between convexity of a metric continuum $X$ and convexity of its hyperspaces $C(X)$ and $2^X$

Duda, R.

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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...

An Exactly Two-to-One Map from an Indecomposable Chainable Continuum

Jerzy Krzempek (2004)

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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.

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Displaying similar documents to “Connexions between convexity of a metric continuum X and convexity of its hyperspaces C ( X ) and 2 X ”

Displaying similar documents to “Connexions between convexity of a metric continuum $X$ and convexity of its hyperspaces $C (X)$ and $2^{X}$ ”