Abstract
In (7.16), a matroid lattice is defined as a compactly atomistic M-symmetric lattice, and it may be defined as an upper continuous AC-lattice. It was shown in (7.10) and (7.15) that in a compactly atomistic lattice (α) the property of being M-symmetric, (β) the covering property, and (γ) the exchange property are equivalent. In DubeilJacotin, Leisieur and Croisot [1] a compactly atomistic lattice with (β) is called a geometric lattice, and in MacLane [1] a compactly atomistic lattice with (γ) is called an exchange lattice.
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References for Chapter III
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Maeda, F., Maeda, S. (1970). Matroid Lattices. In: Theory of Symmetric Lattices. Die Grundlehren der mathematischen Wissenschaften, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46248-1_3
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DOI: https://doi.org/10.1007/978-3-642-46248-1_3
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