Abstract
A frame homomorphism is coz-onto if it maps the cozero part of its domain surjectively onto that of its codomain. This captures the notion of a z-embedded subspace of a topological space in a point-free setting. We give three different types of characterizations of coz-onto homomorphisms. The first is in terms of elements, the second in terms of quotients, and the last in terms of ideals. As an application of properties of coz-onto homomorphisms developed herein, we present some characterizations of \(F\)- and \(F^{\prime }\)-frames.
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Dedicated to Bernhard Banaschewski, on the occasion of his 80th birthday.
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Dube, T., Walters-Wayland, J. Coz-onto Frame Maps and Some Applications. Appl Categor Struct 15, 119–133 (2007). https://doi.org/10.1007/s10485-006-9022-y
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DOI: https://doi.org/10.1007/s10485-006-9022-y