On linear functorial operators extending pseudometrics
For a functor on the category of metrizable compacta, we introduce a conception of a linear functorial operator extending (for each ) pseudometrics from onto (briefly LFOEP for ). The main result states that the functor of -symmetric power admits a LFOEP if and only if the action of on has a one-point orbit. Since both the hyperspace functor and the probability measure functor contain as a subfunctor, this implies that both and do not admit LFOEP.