Theorem Let $\mu$ and $\nu$ are endoreloids. Let $f$ is a principal $\mathrm{C}' ( \mu; \nu)$ continuous, monovalued, surjective reloid. Then if $\mu$ is $\beta$-totally bounded then $\nu$ is also $\beta$-totally bounded.
Theorem Let $\mu$ and $\nu$ are endoreloids. Let $f$ is a principal $\mathrm{C}'' (\mu ; \nu)$ continuous, surjective reloid. Then if $\mu$ is $\alpha$-totally bounded then $\nu$ is also $\alpha$-totally bounded.