This article is cited in 5 papers

One Property of Components of a Chain Recurrent Set

Nikita Shekutkovski

Institute of Mathematics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, 1000 Skopje, Republic of Macedonia

Abstract: For flows defined on a compact manifold with or without boundary, it is shown that the connectivity components of a chain recurrent set possess a stronger connectivity known as joinability (or pointed 1-movability in the sense of Borsuk). As a consequence, the Vietoris–van Dantzig solenoid cannot be a component of a chain recurrent set, although the solenoid appears as a minimal set of a flow.

Keywords: chain recurrent set, continuity in a covering, pointed 1-movability, joinability.

MSC: 54H20, 37B20, 54C56

Received: 04.04.2014

Language: English

DOI: 10.1134/S1560354715020069

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