Sentence:  It is clear that these functions are also the only ones to be <WSD>uniformized</WSD> by the simple mapping of the Riemann surface, for of course any function that is single-valued in "t" must have been, before the mapping, a single-valued function on the Riemann surface. 
Meaning of the word marked with <WSD> tags:  To carry out a process of uniformization, by which a multiple-valued function on a Riemann surface is converted to a single-valued function.