Displaying similar documents to “One-dimensional chain recurrent sets of flows in the 2-sphere.”

On strong chain recurrence for maps

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...

Embeddings of chains into chains

Vítězslav Novák, Tomáš Novotný (2005)

Discussiones Mathematicae - General Algebra and Applications

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Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.

Smooth implications on a finite chain

Yong Su (2019)

Kybernetika

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Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.