We consider de Groot duality for represented spaces. This yields a notion of a dual to a given represented space by identifying a point in X with its closure as an element of A(X). Topologically, we can consider the dual topology as the topology generated by the complements of saturated compact sets. de Groot duality is particularly well-behaved for T_1 spaces, and yields a duality between compact and Hausdorff here. We also have an application to the study of point degree spectra, and can show that the de Groot dual of Baire space is "far from countably based" by using the notion of quasi-minimality. This is (very recent) joint work with Takayuki Kihara.