On discrete and continuous quotient Riesz spaces

被引：0
|
作者：
Wnuk, Witold [1 ]
机构：
[1] Adam Mickiewicz Univ Poznan, Fac Math & Comp Sci, PL-61614 Poznan, Poland
来源：
POSITIVITY | 2011年 / 15卷 / 01期
关键词：
Riesz space; Banach lattice; Locally solid Riesz space; Null ideal; Order bounded operator; LATTICES;
D O I：
10.1007/s11117-009-0042-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Order properties of quotient Riesz spaces E/N(f) by null ideals N(f) are investigated. We show relationships between properties of a Riesz space E and its order dual E similar to and properties of quotients E/N(f) where f runs over some subspaces of E similar to. A characterization of metrizable locally convex topological Riesz spaces whose all quotients (by proper closed ideals) are discrete is also given.
引用
收藏
页码：73 / 85
页数：13
相关论文
共 50 条
  • [11] Riesz* homomorphisms on pre-Riesz spaces consisting of continuous functions
    Hendrik van Imhoff
    Positivity, 2018, 22 : 425 - 447
  • [12] Riesz* homomorphisms on pre-Riesz spaces consisting of continuous functions
    van Imhoff, Hendrik
    POSITIVITY, 2018, 22 (02) : 425 - 447
  • [13] ON QUOTIENT RIESZ ALGEBRAS
    Ilbira, Sabahattin
    Eroglu, Hatice Unlu
    Aydin, Abdullah
    JOURNAL OF SCIENCE AND ARTS, 2024, (01): : 155 - 162
  • [14] Unbounded order continuous operators on Riesz spaces
    Akbar Bahramnezhad
    Kazem Haghnejad Azar
    Positivity, 2018, 22 : 837 - 843
  • [15] Unbounded order continuous operators on Riesz spaces
    Bahramnezhad, Akbar
    Azar, Kazem Haghnejad
    POSITIVITY, 2018, 22 (03) : 837 - 843
  • [16] Statistically order continuous operators on Riesz spaces
    Aydin, Abdullah
    Gorokhova, Svetlana
    Selen, Ramazan
    Solak, Sumeyra
    MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 2023, 17 (01) : 1 - 9
  • [17] QUOTIENT SPACES DETERMINED BY ALGEBRAS OF CONTINUOUS FUNCTIONS
    Lazar, Aldo J.
    ISRAEL JOURNAL OF MATHEMATICS, 2010, 179 (01) : 145 - 155
  • [18] CONTINUOUS MAPPINGS AND QUOTIENT SPACES .1.
    WHITTAKER, JV
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1970, 21 (NOV) : 475 - +
  • [19] Quotient spaces determined by algebras of continuous functions
    Aldo J. Lazar
    Israel Journal of Mathematics, 2010, 179 : 145 - 155
  • [20] Discrete-time stochastic processes on Riesz spaces
    Kuo, WC
    Labuschagne, CCA
    Watson, BA
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2004, 15 (03): : 435 - 451
12345