Extremal representations of polar set and ${M}$-addition
Received date: 2018-08-29
Online published: 2018-12-23
刘畅, 冷岗松 . 极体算子与M-加算子的极表示[J]. 上海大学学报(自然科学版), 2020 , 26(5) : 834 -841 . DOI: 10.12066/j.issn.1007-2861.2092
The extremal representations of the polar set and M-addition are studied. If K is a compact and convex subset of Rn, then we have K° = (ext K)°. It is proved that M-sum of K and L is equal to the (bd M)-sum, if K and $L$ are convex bodies containing the origin and M is a convex body in the first quadrant of R2. Moreover, by the counter-examples given in section 3, all these conditions cannot be removed.
Key words： convex geometry; polar set; $M$-addition; extremal representations
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