We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for ω-languages: Σ_2 , ∆_2 , FO^2∩ Σ_2 (and by duality FO^2∩ Π_2 ), and FO^2. These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke [20] and Bojanczyk [2] and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.