@article{Gong_Reilly_2007, title={On the Order Hereditary Closure Preserving Sum Theorem}, volume={8}, url={https://polipapers.upv.es/index.php/AGT/article/view/1892}, DOI={10.4995/agt.2007.1892}, abstractNote={<p>The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem:</p><p>(1) If a topological property P satisfies (Σ’) and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ϵ V is elementary and possesses P, then X possesses P.</p><p>(2) Let a topological property P satisfy (Σ’) and (β), and be closed hereditary. Let X be a topological space which possesses P. If every open subset G of X can be written as an order hereditary closure preserving (in G) collection of elementary sets, then every subset of X possesses P.</p>}, number={2}, journal={Applied General Topology}, author={Gong, Jianhua and Reilly, Ivan L.}, year={2007}, month={Oct.}, pages={267–272} }