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2 cards from this section. Quick, good the night before a test.
Define a cover in a poset.
Consider the direct relationship without gaps.
What is a maximal element?
Think of elements at the top of the Hasse diagram.
What does a cover require in a poset?
Think about what it means to have no barriers.
True or False: A minimal element can be maximal.
Consider a single node in the diagram.
Construct a poset with at least 5 elements showing both maximal and minimal elements. Prove their existence.
Map relationships that create a hierarchy.
Given a poset, determine if a greatest or least element exists. If it doesn’t, characterize the elements.
Focus on connectivity and relations.
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