Geodesic
Relatively minimal extensions of topological flows
Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 51-65

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The concept of relatively minimal (rel. min.) extensions of topological flows is introduced. Several generalizations of properties of minimal extensions are shown. In particular the following extensions are rel. min.: distal point transitive, inverse limits of rel. min., superpositions of rel. min. Any proximal extension of a flow Y with a dense set of almost periodic (a.p.) points contains a unique subflow which is a relatively minimal extension of Y. All proximal and distal factors of a point transitive flow with a dense set of a.p. points are rel. min. In the class of point transitive flows with a dense set of a.p. points, distal open extensions are disjoint from all proximal extensions. An example of a relatively minimal point transitive extension determined by a cocycle which is a coboundary in the measure-theoretic sense is given.
DOI : 10.4064/cm-84/85-1-51-65
Keywords: factors, flows, topological dynamics

Mieczysław Mentzen 1

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Mieczysław Mentzen. Relatively minimal extensions of topological flows. Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 51-65. doi: 10.4064/cm-84/85-1-51-65

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