Prefix normal words are binary words that have no factor with more 1s than
the prefix of the same length. Finite prefix normal words were introduced in
[Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal
words and explore their relationship to some known classes of infinite binary
words. In particular, we establish a connection between prefix normal words and
Sturmian words, between prefix normal words and abelian complexity, and between
prefix normality and lexicographic order.Comment: 20 pages, 4 figures, accepted at SOFSEM 2019 (45th International
Conference on Current Trends in Theory and Practice of Computer Science,
Nov\'y Smokovec, Slovakia, January 27-30, 2019
