We study the property of openness of the functors for k -nonexpanding and weakly additive functionals. In particular, it is shown that these functors preserve the openness of mappings between finite compact sets but they are not open.
This is a preview of subscription content, log in via an institution to check access.
References
E. V. Shchepin, “Functors and uncountable powers of compact sets,” Usp. Mat. Nauk, 36, 3–62 (1981).
L. Bazylevych, D. Repovˇs, and M. Zarichnyi, “Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces,” Topol. Its Appl., 155, 764–772 (2008).
J. Camargo, “The functor of nonexpanding functionals,” Rev. Integr. Temas Mat., 20, 1–12 (2002).
S. Ditor and L. Eifler, “Some open mapping theorems for measures,” Trans. Amer. Math. Soc., 164, 287–293 (1972).
L. Karchevska and T. Radul, “Some properties of the functor of nonexpanding functionals,” Mat. Stud., 31, 135–141 (2009).
A. Teleiko and M. Zarichnyi, Categorical Topology of Compact Hausdorff Spaces, VNTL Publishers, Lviv (1999).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 11, pp. 1567–1574, November, 2013.
Rights and permissions
About this article
Cite this article
Karchevs’ka, L.I. ON the Openness of Functors of k-Nonexpanding and Weakly Additive Functionals. Ukr Math J 65, 1733–1742 (2014). https://doi.org/10.1007/s11253-014-0892-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0892-0