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On isometric embeddings of Hilbert’s cube into c

Jozef Bobok (1994)

Commentationes Mathematicae Universitatis Carolinae

In our note, we prove the result that the Hilbert’s cube equipped with l p - metrics, p 1 , cannot be isometrically embedded into c .

On isometrical extension properties of function spaces

Hisao Kato (2015)

Commentationes Mathematicae Universitatis Carolinae

In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces C ( Q ) and C ( Δ ) , where Q and Δ denote the Hilbert cube [ 0 , 1 ] and a Cantor set, respectively.

On k -spaces and k R -spaces

Jinjin Li (2005)

Czechoslovak Mathematical Journal

In this note we study the relation between k R -spaces and k -spaces and prove that a k R -space with a σ -hereditarily closure-preserving k -network consisting of compact subsets is a k -space, and that a k R -space with a point-countable k -network consisting of compact subsets need not be a k -space.

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