Displaying similar documents to “Continuous mappings on continua”

Continua determined by mappings.

Charatonik, Janusz J., Charatonik, Wlodzimierz J. (2000)

Publications de l'Institut Mathématique. Nouvelle Série

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Atomicity of mappings.

Charatonik, Janusz J., Charatonik, Włodzimierz J. (1998)

International Journal of Mathematics and Mathematical Sciences

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Absolutely terminal continua and confluent mappings

Janusz Jerzy Charatonik (1991)

Commentationes Mathematicae Universitatis Carolinae

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Interrelations between three concepts of terminal continua and their behaviour, when the underlying continuum is confluently mapped, are studied.

Atomic mappings and extremal continua.

Janusz J. Charatonik (1992)

Extracta Mathematicae

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The notion of atomic mappings was introduced by R. D. Anderson in [1] to describe special decompositions of continua. Soon, atomic mappings turned out to be important tools in continuum theory. In particular, it can be seen in [2] and [5] that these maps are very helpful to construct some special, singular continua. Thus, the mappings have proved to be interesting by themselves, and several of their properties have been discovered, e.g. in [6], [7] and [9]. The reader is referred to...

ω-Limit sets for triangular mappings

Victor Jiménez López, Jaroslav Smítal (2001)

Fundamenta Mathematicae

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In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua...