On non-metric continua that support Whitney maps

We discuss the construction of non-metric continua that support Whitney maps and their properties. We indicate a technique for producing non-metric indecomposable continua that support Whitney maps from certain compact totally disconnected spaces each of which allows a self-homeomorphism all of whose orbits are dense. These are non-metric examples that have the property that each proper subcontinuum is metric. Both perfectly normal and non-perfectly normal examples are constructed. We describe techniques for producing large collections of non-homeomorphic continua that support Whitney maps. An example of a continuum every non-degenerate subcontinuum of which is non-metric that supports a Whitney map is constructed; an example of a continuum that does not support a Whitney map which is the union of two subcontinua each of which supports a Whitney map is constructed.