Geodesic
On free vector balleans
Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 70-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

A vector balleans is a vector space over $\mathbb{R}$ endowed with a coarse structure in such a way that the vector operations are coarse mappings. We prove that, for every ballean $(X, \mathcal{E})$, there exists the unique free vector ballean $\mathbb{V}(X, \mathcal{E})$ and describe the coarse structure of $\mathbb{V}(X, \mathcal{E})$. It is shown that normality of $\mathbb{V}(X, \mathcal{E})$ is equivalent to metrizability of $(X, \mathcal{E})$.
Keywords: coarse structure, ballean, vector ballean, free vector ballean. 
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Igor Protasov; Ksenia Protasova. On free vector balleans. Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 70-74. http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a7/

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