The separability of certain seminormed spaces of harmonic functions on Riemann surfaces will be considered. An application of the result obtained in the above to some inverse inclusion problem in the classification theory of Riemann surfaces will be appended.
"Nonseparability of Banach spaces of bounded harmonic functions on Riemann surfaces." Proc. Japan Acad. Ser. A Math. Sci. 87 (8) 130 - 135, October 2011. https://doi.org/10.3792/pjaa.87.130