Coincidence of maps in Q-simplicial spaces
G. Skordev (1981)
Fundamenta Mathematicae
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G. Skordev (1981)
Fundamenta Mathematicae
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Zdzisław Dzedzej
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CONTENTS0. Introduction.....................................................................5I. Homology.........................................................................6II. Multivalued maps...........................................................11III. Chain approximations and index...................................15IV. Chain approximations of decompositions of maps........18V. Index of decompositions for compact polyhedra............26VI. Index of decompositions for compact...
G. Skordev (1984)
Fundamenta Mathematicae
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Katsuya Yokoi (2015)
Annales Polonici Mathematici
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This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence...
Jonathan Meddaugh, Brian E. Raines (2013)
Fundamenta Mathematicae
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The main result of this paper is that a map f: X → X which has shadowing and for which the space of ω-limits sets is closed in the Hausdorff topology has the property that a set A ⊆ X is an ω-limit set if and only if it is closed and internally chain transitive. Moreover, a map which has the property that every closed internally chain transitive set is an ω-limit set must also have the property that the space of ω-limit sets is closed. As consequences of this result, we show that interval...
Marek Filakovský (2012)
Archivum Mathematicum
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In the paper weak sufficient conditions for the reduction of the chain complex of a twisted cartesian product to a chain complex of free finitely generated abelian groups are found.
Klaus Heiner Kamps (1978)
Colloquium Mathematicae
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Katsuya Yokoi (2007)
Annales Polonici Mathematici
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For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.
Andrew D. Barwell, Gareth Davies, Chris Good (2012)
Fundamenta Mathematicae
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For a continuous map f on a compact metric space (X,d), a set D ⊂ X is internally chain transitive if for every x,y ∈ D and every δ > 0 there is a sequence of points ⟨x = x₀,x₁,...,xₙ = y⟩ such that for 0 ≤ i< n. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an ω-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there...
Lê Minh Hà, Jeffrey Strom (2001)
Fundamenta Mathematicae
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This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set....
(2015)
Archivum Mathematicum
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(2016)
Archivum Mathematicum
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Andrzej Granas (1972)
Bulletin de la Société Mathématique de France
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