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Some categorical properties of the functors O τ and O R of weakly additive functionals

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Abstract

In the paper, the spaces of weakly additive τ-smooth and Radon functionals are investigated. It is proved that the functors of weakly additive τ-smooth and Radon functionals weakly preserve the density of Tychonoff spaces, and the functor of weakly additive τ-smooth functionals forms a monad in the category of Tychonoff spaces and their continuous mappings. Examples and remarks are given showing that these functors fail to satisfy certain Shchepin normality conditions. Problems having positive solutions for normal functors are presented.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Uzbekistan

    A. A. Zaitov

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  1. A. A. Zaitov
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__________

Translated from Matematicheskie Zametki, vol. 79, no. 5, 2006, pp. 681–693.

Original Russian Text Copyright © 2006 by A. A. Zaitov.

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Zaitov, A.A. Some categorical properties of the functors O τ and O R of weakly additive functionals. Math Notes 79, 632–642 (2006). https://doi.org/10.1007/s11006-006-0072-0

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  • DOI: https://doi.org/10.1007/s11006-006-0072-0

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