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Equilateral sets in Banach spaces of the form C(K)

Sophocles K. Mercourakis; Georgios Vassiliadis — 2015

Studia Mathematica

We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.

Isometric embeddings of a class of separable metric spaces into Banach spaces

Sophocles K. Mercourakis; Vassiliadis G. Vassiliadis — 2018

Commentationes Mathematicae Universitatis Carolinae

Let $(M, d)$ be a bounded countable metric space and $c > 0$ a constant, such that $d (x, y) + d (y, z) - d (x, z) \geq c$ , for any pairwise distinct points $x, y, z$ of $M$ . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of $ℓ_{\infty}$ .

Corrigendum to ``Isometric embeddings of a class of separable metric spaces into Banach spaces''

Sophocles K. Mercourakis; Georgios Vassiliadis — 2018

Commentationes Mathematicae Universitatis Carolinae

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Equilateral sets in Banach spaces of the form C(K)

Isometric embeddings of a class of separable metric spaces into Banach spaces

Corrigendum to ``Isometric embeddings of a class of separable metric spaces into Banach spaces''