Characterizing properties of graphs, posets, and even dcpos by forbidden substructures is an intriguing approach. Xiaodong Jia managed to show that every CCC of quasi-continuous domains must consist of continuous domains exclusively, and I would like to explain how this rests on the very ingenious idea that one should study meet-continuous dcpos, and specifically, that one can characterize non-meet-continuous dcpos through certain forbidden substructures. Read the full post.