Injective compact distributive lattices Academic Article uri icon

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abstract

  • In the category of zero-dimensional compact distributive lattices and their continuous lattice-homomorphisms, it is firstly shown that the injective objects are precisely the compact Boolean algebras, and each object has an injective envelope. Secondly, it is shown that the category of compact distributive lattices and their continuous lattice-homomorphisms has no non-trivial injective object.

publication date

  • January 1, 1973