On Regular Riesz Subspaces
- Witold Wnuk
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The paper is devoted to investigations of properties of regular Riesz subspaces and connections between regularity and some topological properties. The problem if a topological closure preserves regularity is solved in the class of discrete Riesz spaces. We also characterize Dedekind complete Riesz spaces possessing the same classes of σ-regular and regular Riesz subspaces Moreover, various examples of regular and non regular Riesz spaces are presented.
- Aliprantis, C. and Burkinshaw, O.: Locally Solid Riesz Spaces, in Pure and Applied Mathematics Series no. 76, Academic Press, New York, San Francisco, London, 1978.
- Aliprantis, C. and Burkinshaw O.: Minimal topologies and Lp-spaces, Illinois J. Math. 24 (1980), 164–172.
- Fremlin, D.H.:Topological Riesz Spaces and Measure Theory,Cambridge University Press, London, New York, 1974.
- Luxemburg, W.A.J. and Zaanen, A.C.Riesz Space I, North Holland, Amsterdam, London. 1971.
- Mekler, A.A.: On embeddings of vector lattices preserving suprema and infima, Leningrad. Gos. Ped. Inst.. XXIV Hercen Meeting, 1971,pp.54–56 (in Russian).
- Mekler, A.A. and Sokolovskaya, N.F.: Subspaces in Nakano's sense of conditionaly complete vector lattices, in: Functional analysis. Spectral Theory, No.18, Ul'janovsk. Gos. Ped. Inst., Ul'janovsk, 1982, pp. 92–101 (in Russian).
- Wnuk, W.: When is the closure of an atomic Riesz subspace atomic?. Bull. Ac. Pol.: Math. 34 (1986), 689–694.
- Wnuk, W.: Remarks on a structure of Banach lattices. Atti Sem. Mat. Fis. Univ. Modena 44 (1986),359–371.
- Wnuk, W.: Banach Lattices with Order Continuous Norms, in: Advanced Topics in Mathematics,Polish Scientific Publishers PWN, Warszawa, 1999.
- On Regular Riesz Subspaces
Volume 7, Issue 1-2 , pp 33-40
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- regular Riesz subspace
- σ-regular Riesz subspace
- locally solid Riesz spaces
- countable sup property
- Lebesgue property
- Witold Wnuk (1)
- Author Affiliations
- 1. Faculty of Mathematics and Computer Science, A. Mackiewicz University, Umultowska 87, Poznań, Poland