Topological lattices with small semilattices

I would like to explain a clever counterexample due to Jimmie Lawson in 1970, or rather a slight variant of it, pertaining to the theory of topological semilattices and to a property that crops up naturally, namely having small semilattices. Before I can do this, I will have to spend some time explaining what topological semilattices are, and how small semilattices arise naturally. For motivational purposes, I will consider the problem of characterizing the algebras of the so-called finitary Smyth hyperspace monad, a question that Andrea Schalk has solved, among others, in her 1993 PhD thesis. Read the full post.

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