Abstract Convexity and
Cone-Vexing Abstractions

S. S. Kutateladze

The slides are available in PDF.

This talk 1 is devoted to some origins of abstract convexity and a few vexing limitations on the range of abstraction in convexity. Convexity is a relatively recent subject. Although the noble objects of Euclidean geometry are mostly convex, the abstract notion of a convex set appears only after the Cantor paradise was founded. The idea of convexity feeds generation, separation, calculus, and approximation. Generation appears as duality; separation, as optimality; calculus, as representation; and approximation, as stability. Convexity is traceable from the remote ages and flourishes in functional analysis.


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[6] Singer I. (1997) Abstract Convex Analysis. New York: John Wiley & Sons.
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[10] Fuchssteiner B. and Lusky W. (1981) Convex Cones. Amsterdam: North-Holland.
[11] Kusraev A. G. and Kutateladze S. S. (2007) Subdifferential Calculus: Theory and Applications. Moscow: Nauka Publishers [in Russian].
[12] Dilworth S. J., Howard R., and Roberts J. W. (2006) A general theory of almost convex functions. Trans. Amer. Math. Soc., 358:8, 3413–3445.


1 Delivered on August 26, 2007, at the International Workshop on the Idempotent and Tropical Mathematics in Moscow, August 26–30, 2007. I am grateful to Professor G. Litvinov who kindly invited this talk to the “tropics.”

Mathematics, abstract arXiv:0705.2793

File translated from TEX by TTH, version 3.77.
On 18 May 2007, 09:01.

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