, Volume 7, Issue 1, pp 33-40

First online:

On Regular Riesz Subspaces

  • Witold WnukAffiliated withFaculty of Mathematics and Computer Science, A. Mackiewicz University

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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.

regular Riesz subspace σ-regular Riesz subspace locally solid Riesz spaces countable sup property Lebesgue property