Open mapping theorem for spaces of weakly additive homogeneous functionals

Author: Zaitov, A.

Source: Mathematical Notes, Volume 88, Numbers 5-6, December 2010 , pp. 655-660(6)

Publisher: Springer

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Abstract:

We establish that if X and Y are metric compacta and f: X → Y is a continuous surjective mapping, then the openness of the mapping OH(f): OH(X) → OH(Y) of spaces of weakly additive homogeneous functionals is equivalent to the openness of f.

Keywords: open mapping theorem; metric compactum; weakly additive homogeneous functional; probability measure; topology of pointwise convergence

Document Type: Research article

DOI: http://dx.doi.org/10.1134/S0001434610110052

Affiliations: 1: Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan, Email: adilbek_zaitov@mail.ru

Publication date: 2010-12-01