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Reduced Lattices

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2032)

Abstract

Recall that a poset P is said to be a lattice if every two-point set {a, b} has a least upper bound ab, called join or supremum of a and b, and a greatest lower bound ab, 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.

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© 2011 Springer-Verlag Berlin Heidelberg

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Barmak, J.A. (2011). Reduced Lattices. In: Algebraic Topology of Finite Topological Spaces and Applications. Lecture Notes in Mathematics(), vol 2032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22003-6_9

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