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Komiya, Hidetoshi

Closedness of cones. (English) Zbl 0494.46006

J. Math. Anal. Appl. 81, 320-326 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0494.46006

MSC:

46A40 Ordered topological linear spaces, vector lattices
46A55 Convex sets in topological linear spaces; Choquet theory
52A07 Convex sets in topological vector spaces (aspects of convex geometry)

Keywords:

cones in topological vector spaces; closed cones; cones generated by a set; quotient topology; pi-convexity
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References:

[1] Braunschweiger, C. C.; Clark, H. F., An extension of the Farkas theorem, Amer. Math. Monthly, 69, 272-277 (1962) · Zbl 0116.08302
[2] Braunschweiger, C. C., An extension of the nonhomogeneous Farkas theorem, Amer. Math. Monthly, 69, 969-975 (1962) · Zbl 0108.10702
[3] Fan, K., On systems of linear inequalities, (Linear Inequalities and Related Systems. Linear Inequalities and Related Systems, Annals of Math. Studies 38 (1956), Princeton Univ. Press), 99-1956 · Zbl 0072.37602
[4] Klee, V. L., Separation properties of convex cones, (Proc. Amer. Math. Soc., 6 (1955)), 313-318 · Zbl 0064.35602
[6] Kőthe, G., Topological Vector Spaces I (1969), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0179.17001
[7] Stoer, J.; Witzgal, C., Convexity and Optimization in Finite Dimensions I (1970), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0203.52203
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