Meet-continuous spaces

Meet-continuous dcpos were defined and studied by Hui Kou, Ying-Ming Liu, and Mao-Kang Luo about 14 years ago, and their importance only starts to be appreciated now.  One of the leading results in the theory of meet-continuous dcpos is that a dcpo is continuous if and only if it is quasi-continuous and meet-continuous.  Weng Kin Ho, Achim Jung and Dongsheng Zhao’s gave a new proof of that theorem through Stone duality.  Today, I would like to talk about yet another proof, which I had the pleasure to read in Xiaodong Jia‘s remarkable PhD thesis. Read the full post.