Geodesic
Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 531-542

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A subspace $I_f(X)$ of the space of idempotent probability measures on a given compact space $X$ is constructed. It is proved that if the initial compact space $X$ is contractible, then $I_f(X)$ is a contractible compact space as well. It is shown that the shapes of the compact spaces $X$ and $I_f(X)$ are equal. It is also proved that, given a compact space $X$, the compact space $I_f(X)$ is an absolute neighborhood retract if and only if so is $X$.
Keywords: idempotent measure, compact space, absolute neighborhood retract, shape. 
@article{MZM_2019_106_4_a4,
     author = {A. A. Zaitov and A. Ya. Ishmetov},
     title = {Homotopy {Properties} of the {Space} $I_f(X)$ of {Idempotent} {Probability} {Measures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {531--542},
     publisher = {mathdoc},
     volume = {106},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/}
}
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A. A. Zaitov; A. Ya. Ishmetov. Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 531-542. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a4/