Normal functors in the category of ultrametric spaces

Анотація

We show that every normal functor acting in the category of compact Hausdorff spaces COMP determines a functor in the category UMET of ultrametric spaces and nonexpanding maps. Some properties of the obtained functors in UMET are established. In particular, we show that these functors preserve the class of complete ultrametric spaces; this fact was already known for the hyperspace functor and the probability measure functor. We show also that every natural transformation of normal functors in COMP determines a natural transformation of the corresponding functors in UMET.