Two theorems about totally bounded images of a totally bounded reloid

I’ve added to my book two following theorems (formerly conjectures).

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.

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