( 289 j 
.. . . . two Dlt)D er arcs, and not into two improper ones'). 
"shat now consider on’ each of the cnrves * and the 
cyclically ordered sets u and u' of their outwardly accessible points. 
These determine on each other certain segments o„ and.<J„, forming 
in pairs certain cyclically ordered sets of po uts from a 
rest region of 0 and O', as is schematically illustrated by tig. . 
If we make a circuit along u and u' together in sue senses, 
that segments o„ and o', are reached simultaneously, this circuit 
made in opposite senses for u and u'. 
So if we make a circuit along u and u' together in such a way 
that points corresponding for the transformationarereachedsim^- 
taneously, then with respect to the former order they must meet 
twice in that course, and at such a meeting either corresponding 
~) For these notions comp. L. E. J. Brouwer, “Zur Analyst SiiiKl” 
ein-emdeutige stetige Transformationen von Fldchen m sich , Mat it 
and “Ueber 
m. Annalen, 
