Homotopy properties of the space OS_f(X)

2020/03/17 by Kh. ~Kh. ~Kurbanov, ~Kurbanov, Kh. ~Kh., A. ~Ya. ~Ishmetov +1
Mathematics · #52A30 #54C65 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:52A30 #msc:54C65

paper · pdf · doi:10.48550/arxiv.2003.07744

12 pages

arxiv created 2020/03/17 · arxiv updated 2020/11/13

Abstract

For a given compact Hausdorff space X, we construct the space OS_f(X) of normed, order-preserving, weakly additive, positively homogeneous and semi-additive functionals (for brevity, semi-additive functionals) and it is proved that the hyperspace exp X of the space X is a deformation retract of the constructed space. Further we show that the shapes of the spaces OS_f(X) and exp X coincide. We establish that if the space exp X is contractible, then the space OS_f(X) is also contractible.

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