TY - JOUR
AU - Gong, Jianhua
AU - Reilly, Ivan L.
PY - 2007/10/01
Y2 - 2024/10/12
TI - On the Order Hereditary Closure Preserving Sum Theorem
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 8
IS - 2
SE -
DO - 10.4995/agt.2007.1892
UR - https://polipapers.upv.es/index.php/AGT/article/view/1892
SP - 267-272
AB - <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>
ER -