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Tag Archives: algebra
Algebras of filter-related monads: II. KZ-monads
Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category Top0 of T0 topological spaces are exactly the continuous (complete) lattices. Martín Escardó later gave a very interesting proof of this fact, using a category-theoretic construction … Continue reading
Posted in Uncategorized
Tagged algebra, continuous lattice, filter, monad
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Algebras of filter-related monads: I. Ultrafilters and Manes’ theorem
In 1969, Ernest Manes proved the following remarkable result: the algebras of the ultrafilter monad on Set are exactly the compact Hausdorff spaces. This is remarkable, because it gives a purely algebraic/category-theoretic of the otherwise purely topological notion of compact … Continue reading
Posted in Uncategorized
Tagged algebra, compactness, filter, monad
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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. … Continue reading
Posted in Uncategorized
Tagged algebra, hyperspace, lattice, monad, powerdomain, semilattice
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