Abstract:
We establish that if $X$ and $Y$ are metric compacta and $f\colon X\to Y$ is a continuous surjective mapping, then the openness of the mapping $OH(f)\colon OH(X)\to OH(Y)$ 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.
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