ALGEBRAIC AND TOPOLOGICAL THEORY OF LANGUAGES

A language is torsion (resp. bounded torsion, aperiodic, bounded aperi odic), if its syntactic monoid is torsion (resp. bounded torsion, aper iodic, bounded aperiodic). We generalize the regular language theorems of Klenne, Schutzenberger and Straubing to describe the classes of to rsion, bounded torsion, aperiodic and bounded aperiodic languages. The se descriptions involve taking limits of sequences of languages and au tomata for certain topologies defined by filtrations of the free monoi d. A theorem for arbitrary languages over finite alphabets is also sta ted and proved.