Well-filtered dcpos

Posted on June 17, 2017 by jgl

I have just returned from the International Symposium on Domain Theory, which took place in Shijiazhuang, Hebei, China.  That was a fine conference indeed.  There, I met Xiaoyong Xi and Jimmie Lawson, who just happened to publish a remarkable result, related to a very recent post on coherence of dcpos: every complete lattice, and more generally every bounded-complete dcpo is well-filtered in its Scott topology.  Read the full post.

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One Response to Well-filtered dcpos

  1. xiaodong.jia says:
    June 18, 2017 at 9:18 pm

    With this post, the counterexample in your last post is now easier to understand. The natural numbers with the cofinite topology is not well-filtered, so any bounded complete dcpo, which is well-filtered in the Scott topology, cannot be a dcpo model of it.

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