Displaying similar documents to “A characterization of paracompactness”

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...

Weak chain-completeness and fixed point property for pseudo-ordered sets

S. Parameshwara Bhatta (2005)

Czechoslovak Mathematical Journal

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In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.

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.