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

Infinite Reduced Words, Lattice Property And Braid Graph of Affine Weyl Groups