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Post Closed as "Needs details or clarity" by Stefan Kohl, Stefan Waldmann, Daniel Moskovich, Ricardo Andrade, Emil Jeřábek
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Todd Trimble
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A lattice structure requires that every two elements have a join and a meet. Suppose I have such a posetwe consider instead posets in which for every two elements $x,y$, if there exists an element greater than both of them, then their join exists, and if there exists an element smallerless than both of them, then their meet exists. What can be said about such posets?

Thanks

A lattice structure requires that every two elements have a join and a meet. Suppose I have such a poset in which for every two elements $x,y$, if there exists an element greater than both of them, then their join exists, and if there exists an element smaller than both of them, then their meet exists. What can be said about such posets?

Thanks

A lattice structure requires that every two elements have a join and a meet. Suppose we consider instead posets in which for every two elements $x,y$, if there exists an element greater than both of them, then their join exists, and if there exists an element less than both of them, then their meet exists. What can be said about such posets?

Thanks

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Todd Trimble
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A lattice structure requires that every two elements have a join and a meet. IfSuppose I have such a structureposet in which for every two elements x$x,y$,y if there exists an element z greater than both of them, therethen their join exists a supremum, and if there exists an element smaller than both of them there, then their meet exists an infimum. what propertiesWhat can I know on this structure.be said about such posets?

Thanks

A lattice structure requires that every two elements have a join and a meet. If I have such a structure in which for every two elements x,y if there exists an element z greater than both of them, there exists a supremum, and if there exists an element smaller than them there exists an infimum. what properties can I know on this structure.

Thanks

A lattice structure requires that every two elements have a join and a meet. Suppose I have such a poset in which for every two elements $x,y$, if there exists an element greater than both of them, then their join exists, and if there exists an element smaller than both of them, then their meet exists. What can be said about such posets?

Thanks

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Avi
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What properties of lattice are preserved in a weak lattice structure

A lattice structure requires that every two elements have a join and a meet. If I have such a structure in which for every two elements x,y if there exists an element z greater than both of them, there exists a supremum, and if there exists an element smaller than them there exists an infimum. what properties can I know on this structure.

Thanks