%0 Journal Article
%T Prethick subsets and partitions of metric spaces
%A K. D. Protasova
%J Matematychni Studii
%D 2012
%I Lviv Mathematical Society, VNTL Publishers
%X A subset $A$ of a metric space $(X,d)$ is called thick if, forevery $r>0$, there is $ain A$ such that $B_{d}(a,r)subseteqA,$ where $B_{d}(a,r)={xin Xcolon d(x,a)leq r}$. We showthat if $(X, d)$ is unbounded and has no asymptoticallyisolated balls then, for each $r>0$, there exists a partition$X=X_{1}cup X_{2}$ such that $B_{d}(X_{1},r)$ and$B_{d}(X_{2},r)$ are not thick.
%K metric space
%K thick and prethick subsets
%K asymptotically isolated balls
%U http://matstud.org.ua/texts/2012/38_2/115-117.pdf