  In this paper, we establish a bijection between the infinite reduced words of
an affine Weyl group and certain biclosed sets of its positive system and
determine all finitely generated biclosed sets in the positive system of an
affine Weyl group. Using these results, we show first that the biclosed sets in
the standard positive system of rank 3 affine Weyl groups when ordered by
inclusion form a complete algebraic ortholattice and secondly that the
(generalized) braid graphs of those Coxeter groups are connected, which can be
thought of as an infinite version of Tit's solution to the word problem.
