Faigle, Ulrich Extensions and duality of finite geometric closure operators. (English) Zbl 0434.06004 J. Geom. 14, 23-34 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 06A06 Partial orders, general 06A15 Galois correspondences, closure operators (in relation to ordered sets) Keywords:finite partially ordered set; geometric closure operator PDF BibTeX XML Cite \textit{U. Faigle}, J. Geom. 14, 23--34 (1980; Zbl 0434.06004) Full Text: DOI OpenURL References: [1] Birkhoff, G.: Abstract linear dependence and lattices. Amer. J. Math.57 (1935), 800–804. · JFM 61.1027.01 [2] Brylawski, T.H.: A decomposition for combinatorial geometries. Trans. A.M.S.171 (1972), 235–282. · Zbl 0224.05007 [3] Crapo, H.: Single-element extensions of matroids. J. Res. Nat. Bur. Standards69B (1965), 55–65. · Zbl 0141.21701 [4] Crapo, H. and Rota, G.-C., Combinatorial Geometries, M.I.T. Press, Cambridge, Mass., 1970. · Zbl 0216.02101 [5] Dilworth, R.P.: Dependence relations in a semi-modular lattice. Duke Math. J.8 (1944), 575–578. · Zbl 0060.06101 [6] Faigle, U.: Geometries on partially ordered sets. To appear: J. Comb. Th. B. · Zbl 0359.05018 [7] Faigle, U.: Über Morphismen halbmodularer Verbände. Aequat. Math.19 (1979). · Zbl 0443.06009 [8] Finkbeiner, D.T.: A general dependence relation for lattices. Proc. A.M.S.2 (1951), 756–759. · Zbl 0044.02101 [9] Whitney, H.: On the abstract properties of linear dependence. Amer. J. Math.57 (1935), 73–84. · Zbl 0012.00404 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.