Characterization of union of DCFLs We know that DCFL is not closed under the union operation and
CFL is closed under union and contains the union of DCFLs.

Is there a characterization of finite unions of DCFLs?
One direction is clear:  the union of any finite number of DCFL's is a CFL.  

However, a precise characterization of the union-closure of DCFL's was not obvious to me at all (and I teach this stuff and wrote a book on it), so I went searching with a google search.  I found this paper by my colleagues  Martin Kutrib and Andreas Malcher:   Context-Dependent Nondeterminism for Pushdown Automata, O.H. Ibarra and Z. Dang (Eds.): DLT 2006, LNCS 4036, pp. 133–144, 2006.  Theorem 1 gives a characterization of this class.