Geodesic
On the Dimension of the Space of Weakly Additive Functionals
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 347-359

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Important demanded properties of weakly additive order-preserving normalized functionals are established. Various interpretations of a weakly additive order-preserving normalized functional are given. The continuity of such a functional as a function depending on a set in a given compact space is proved. Based on these results, an example is constructed showing that the space $O(X)$ of weakly additive order-preserving normalized functionals is not embedded in any space of finite (or even countable) algebraic dimension, provided that the compact space $X$ contains more than one point.
Keywords: space of weakly additive functionals, functor of weakly additive functionals
Mots-clés : dimension. 
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     author = {R. E. Jiemuratov},
     title = {On the {Dimension} of the {Space} of {Weakly} {Additive} {Functionals}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a2/}
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R. E. Jiemuratov. On the Dimension of the Space of Weakly Additive Functionals. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 347-359. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a2/