( 785 ) 
of medicina forensis henceforth maintain its position by the side of 
the precipitation in vitro as a valuable method. 
Among the many questions that show themselves in the study of 
our subject, there was also the following: what happens to the 
injected horse-serum during the anaphylactic shock? If there were 
only a minimal quantity free and unchanged in the circulation of 
the intoxicated animal, it ought to be possible that with its blood a 
normal animal could be sensitized. Now it has appeared to me that 
this is never crowned with success. From this it may be inferred that 
all the antigen taken up in the blood-circulation is at once fixed by 
the cells of the hypersensitive organism, resp. deprived of its specific 
character at the same time. 
Mathematics. — “On the structure of perfect sets of points ”. By 
Dr. L. E. J. Brouwer. (Communicated by Prof. Kortkwkg). 
(Communicated in the meeting of March 26, 1909). 
M- 
Sets of points and sets of pieces. 
The sets of points discussed in the following lines are supposed 
to be lying within a finite domain of a Sp tt - 
By a piece of a closed set of points ft we understand a single 
point or closed coherent set of points, belonging to fi, and not con¬ 
tained in an other closed coherent set of points belonging to g. 
We can regard as elements of ft its pieces as well as its points, 
in other words we can consider g on one hand as a set of points , 
on the other hand as a set of pieces. 
Let us choose among the pieces of ft a fundamental series S x , S«, 
S t ,.. ., then to ft belong one or more pieces X S U , ... with the 
property that S n lies entirely within a for indefinitely increasing n 
indefinitely decreasing distance e n from one of the pieces a &. These 
parts we shall call the limiting pieces of the fundamental series 
Sl, As’ thus the set g possesses to each of its fundamental series of 
pieces at least one limiting piece, a closed set of points is likewise closed 
as set of pieces. 
By an Mated piece of (* we understand a piece having from its 
rest set in p a finite distance, in other words a piece, the rest set of 
which is closed. 
