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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Reduced Lattices
verfasst von : Jonathan A. Barmak
Erschienen in: Algebraic Topology of Finite Topological Spaces and Applications
Verlag: Springer Berlin Heidelberg
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Recall that a poset P is said to be a lattice if every two-point set {a, b} has a least upper bound a ∨ b, called join or supremum of a and b, and a greatest lower bound a ∧ b, called meet or infimum. Any finite lattice has a maximum (and a minimum), and in particular it is a contractible finite space. In this chapter we will study the spaces obtained from a lattice by removing its maximum and its minimum, which are more attractive from a topological point of view.