Displaying similar documents to “Diagonal-like embeddings”

On positive embeddings of C(K) spaces

Grzegorz Plebanek (2013)

Studia Mathematica

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We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such...

On tame embeddings of solenoids into 3-space

Boju Jiang, Shicheng Wang, Hao Zheng, Qing Zhou (2011)

Fundamenta Mathematicae

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Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ which are strictly achiral. Since solenoids...