  Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space
by closed subsets of another space are introduced. It is shown that, for each
pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous
representations is a lattice and a compact Hausdorff Lawson upper semilattice.
The categories of ambiguous and $L$-ambiguous representations are defined and
investigated.
