  We discuss the regimes of quantum degeneracy in a trapped 1D gas and obtain
the diagram of states. Three regimes have been identified: the BEC regimes of a
true condensate and quasicondensate, and the regime of a trapped gas of Tonks
(gas of impenetrable bosons). The presence of a sharp cross-over to the BEC
regime requires extremely small interaction between particles. We discuss how
to distinguish between true and quasicondensates in phase coherence
experiments.
