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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...

Embedding of the ordinal segment [ 0 , ω 1 ] into continuous images of Valdivia compacta

Ondřej F. K. Kalenda (1999)

Commentationes Mathematicae Universitatis Carolinae

We prove in particular that a continuous image of a Valdivia compact space is Corson provided it contains no homeomorphic copy of the ordinal segment [ 0 , ω 1 ] . This generalizes a result of R. Deville and G. Godefroy who proved it for Valdivia compact spaces. We give also a refinement of their result which yields a pointwise version of retractions on a Valdivia compact space.

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