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| Volume 4, Number 3, September 2008, pp. 465-481 | |||||||||
| Emil Ernst and Michel Volle | |||||||||
| Key words: | |||||||||
| anticonvex set, radially anticonvex set, radially anticonvex function, infinity cone, infinity functions, recession analysis | |||||||||
| Mathematices Subject Classification: 26B99, 46N10, 49J99 | |||||||||
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| Abstract: | |||
| In the real vector space setting, we prove that any apex-containing cone whose apex is the null vector is the infinity cone of some set. Moreover, we introduce an infinity mapping notion such that any 1-homogeneous extended-real-valued function not identically equal to +∞ coincides with the infinity mapping to some extended-real-valued function. These results heavily rely on the properties of two newly introduced objects, the radially anticonvex sets and the radially anticonvex functions. | |||
| Infinity cones and functions in real vector spaces: an existence result | ||