## $$\mathcal {Z}$$-distributive function lattices.(English)Zbl 1289.06009

For a non-empty space $$X$$ and a non-trivial lattice $$Y$$, some connections between properties of the poset $$[X,Y]$$ of all continuous functions $$X\to Y$$ and properties of $$X$$ and $$Y$$ are well known. For instance, $$[X,Y]$$ is a continuous lattice if, and only if, both $$Y$$ and $$\mathcal {O}X$$ are continuous lattices. In the article this result is extended to certain classes of $$\mathcal {Z}$$-distributive lattices, where $$\mathcal {Z}$$ is the Wright-Wagner-Thatcher subset system. While this is likely to be the main aim of the article, other results of a similar nature are obtained as well.
Reviewer: Ittay Weiss (Suva)

### MSC:

 06B35 Continuous lattices and posets, applications 06D10 Complete distributivity 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54H10 Topological representations of algebraic systems
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