Characterizations of Riesz spaces with b-property
POSITIVITY, cilt.13, sa.1, ss.21-30, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 13 Sayı: 1
- Basım Tarihi: 2009
- Doi Numarası: 10.1007/s11117-008-2227-6
- Dergi Adı: POSITIVITY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.21-30
- Anahtar Kelimeler: Riesz spaces, b-property, locally solid Riesz spaces, Levi property
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
A Riesz space E is said to have b-property if each subset which is order bounded in E(similar to similar to) is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology vertical bar sigma vertical bar (E(similar to), E) is studied. Perfect Riesz spaces are characterized in terms of b-property. It is shown that b-property coincides with the Levi property in Dedekind complete Frechet lattices.