Classification of semispaces according to their types in infinite-dimensional vector spaces

被引：4

作者：

Gorokhovik, VV ^{[1
]}

Semenkova, EA ^{[1
]}

机构：

[1] Belarusian State Univ, Inst Math, Minsk 220050, BELARUS

来源：

MATHEMATICAL NOTES | 1998年 / 64卷 / 1-2期

关键词：

vector space; semispace; classification of semispaces; cut of a completely preordered space; jump; Dedekind cuts; gap; pointed cone; convex set;

D O I：

10.1007/BF02310300

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that each semispace C subset of X naturally generates a relation of complete preorder on X with respect to which the pair (X \ C, C) is a cut of X. By identifying the type of the semispace with the type of the cut generated by this semispace, the semispaces are classified according to their types. The obtained classification extends the classification of semispaces in finite-dimensional vector spaces due to Martinez-Legaz and Singer to infinite-dimensional spaces.

引用

页码：164 / 169

页数：6

共 12 条

[1] ALEKSANDROV PS, 1977, INTRO SET THEORY GEN
[2] GOROKHOVIK VV, 1990, CONVEX PROBLEMS VECT
[3] MAXIMAL CONVEX SETS
HAMMER, PC
[J]. DUKE MATHEMATICAL JOURNAL, 1955, 22 (01) : 103 - 106
[4] Kakutani S., 1938, P IMP ACAD JAPAN, V14, P93, DOI 10.3792/pia/1195579980
[5] Klee V.L., 1956, MATH SCAND, V4, P54, DOI [DOI 10.7146/MATH.SCAND.A-10455, 10.7146/math.scand.a-10455]
[6] CONVEX HALF-SPACES
LASSAK, M
[J]. FUNDAMENTA MATHEMATICAE, 1984, 120 (01) : 7 - 13
[7] RECESSION CONES AND THE DOMINATION PROPERTY IN VECTOR OPTIMIZATION
LUC, DT
[J]. MATHEMATICAL PROGRAMMING, 1990, 49 (01) : 113 - 122
[8] Martinez-Legaz JE., 1983, Zeitschr Fur Oper Res, V27, P257
[9] LEXICOGRAPHICAL ORDER, LEXICOGRAPHICAL INDEX, AND LINEAR-OPERATORS
MARTINEZLEGAZ, JE
SINGER, I
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 128 : 65 - 95
[10] THE STRUCTURE OF HEMISPACES IN RN
MARTINEZLEGAZ, JE
SINGER, I
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 110 : 117 - 179

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