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Ellis groups of quasi-factors of minimal flows

Joseph Auslander (2000)

Colloquium Mathematicae

A quasi-factor of a minimal flow is a minimal subset of the induced flow on the space of closed subsets. We study a particular kind of quasi-factor (a 'joining' quasi-factor) using the Galois theory of minimal flows. We also investigate the relation between factors and quasi-factors.

Embedding a topological group into a connected group

Ryo Ohashi (2007)

Colloquium Mathematicae

It was proved in [HM] that each topological group (G,·,τ) may be embedded into a connected topological group (Ĝ,•,τ̂). In fact, two methods of introducing τ̂ were given. In this note we show relations between them.

Embedding into discretely absolutely star-Lindelöf spaces

Yan-Kui Song (2007)

Commentationes Mathematicae Universitatis Carolinae

A space X is discretely absolutely star-Lindelöf if for every open cover 𝒰 of X and every dense subset D of X , there exists a countable subset F of D such that F is discrete closed in X and St ( F , 𝒰 ) = X , where St ( F , 𝒰 ) = { U 𝒰 : U F } . We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.

Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms

Sarah Holte (1995)

Colloquium Mathematicae

In this paper we address the following question due to Marcy Barge: For what f:I → I is it the case that the inverse limit of I with single bonding map f can be embedded in the plane so that the shift homeomorphism f ^ extends to a diffeomorphism ([BB, Problem 1.5], [BK, Problem 3])? This question could also be phrased as follows: Given a map f:I → I, find a diffeomorphism F : 2 2 so that F restricted to its full attracting set, k 0 F k ( 2 ) , is topologically conjugate to f ^ : ( I , f ) ( I , f ) . In this situation, we say that the inverse...

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