If a set is not a convex set, then it is called a non-convex set. While some authorities proscribe the use of "concave set" as a synonym for this, others advocate it. In addition, a polygon that is not a convex polygon may sometimes be called a concave polygon.
With proper choice of universe, it can be useful to define a concave set as a set whose complement is a convex set.
- Takayama, Akira (1994), Analytical Methods in Economics, University of Michigan Press, p. 54, ISBN 9780472081356, "An often seen confusion is a "concave set". Concave and convex functions designate certain classes of functions, not of sets, whereas a convex set designates a certain class of sets, and not a class of functions. A "concave set" confuses sets with functions."
- Corbae, Dean; Stinchcombe, Maxwell B.; Zeman, Juraj (2009), An Introduction to Mathematical Analysis for Economic Theory and Econometrics, Princeton University Press, p. 347, ISBN 9781400833085, "There is no such thing as a concave set."
- Weisstein, Eric W. "Concave." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Concave.htm
- McConnell, Jeffrey J. (2006), Computer Graphics: Theory Into Practice, p. 130, ISBN 0-7637-2250-2.
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