CERTAIN PROPERTIES PRESERVED BY PROPER SUBSPACES

In [3] F .Arenas studied some properties having the property: (*)If every proper subspace has the property, the whole space has the property. In [3], F. Arenas studied some properties such as: Ti -space; i = 0, 1, 2, 3, countability axioms and metrizability. Also in [1] and [2] Al-Bsoul studied some other properties having the property (*) such as: nonfamiliar separation axioms, paracompact, metacompact, collectionwise normal, Baire spaces, ^-spaces, ct -compact, sequentially compact, hemicompact, 8-normal, pseudo compact and extremely disconnected. In this paper we study more properties that preserved by proper subspaces, like: H-closed, a -compact, quasi-^-spaces, almost paracompact, semi regular, minimal Housdorff, fully normal, sequential, Freshet, monotonically normal and expandable spaces. Where we give the answers of two questions that was raised in [2].