Properties of Theta-closure in L-Spaces

Theta-closure is an important tool for investigation of L-Hausdorff separability, regular separability and H-sets in L-spaces. In this paper, we generalize it to L-spaces and systematically explore the properties of theta-closure, theta-interior and theta-closed sets. Constructions and some characteristic descriptions are formulated. It is proved that theta-closed sets are multiplicative, hereditary and invariant in closed continuous order homomorphism.