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An approach to covering dimensions

Miroslav Katětov (1995)

Commentationes Mathematicae Universitatis Carolinae

Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.

An attraction result and an index theorem for continuous flows on n × [ 0 , )

Klaudiusz Wójcik (1997)

Annales Polonici Mathematici

We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on E = n + 1 for which E = n × 0 is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on n × [ 0 , ) .

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