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

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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. 
@article{ADM_2019_27_1_a7,
     author = {Igor Protasov and Ksenia Protasova},
     title = {On free vector balleans},
     journal = {Algebra and discrete mathematics},
     pages = {70--74},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a7/}
}
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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/