Injective Compact Distributive Lattices

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1973Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 37, page 241 (issn: 0002-9939,

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Authors: Choe, Tae Ho;

doi: 10.2307/2038741 , 10.1090/s0002-9939-1973-0309818-0

Injective Compact Distributive Lattices

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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.

Keywords

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, Structured objects in a category

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