id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-1204	Majeed, R. N.; Nasir, A. I.	Some Results on Semi-preopen Sets	2017	6	.pdf	application/pdf	2223	121	90	�� ح Since for all αخL, Aα is semi- preopen , therefore there exists Uα خPO(X) such that �� ح �� ح ���, and since ⋃ ���∈� is a preopen set (by theorem 1.3 ), therefore let U = ⋃ ���∈� ,then we get U ح ⋃ ���∈� ………… (1) Now since �� ح ��� for all αخL, therefore ⋃ ���∈� ⋃ ح Lخ���� for all αخL, implies ⋃ Lخ� �� ⋃ ح Lخ��� ����������� for all αخL, thus ⋃ Lخ� �� �� ح = ⋃ Lخ��� ����������� ….. (2) and from (1) and (2) we get, there exists UخPO(X) such that U ح ⋃ �� �∈� ⋃ therefore ,�� ح �∈� �� is semi-preopen set.	cache/iajs-1204.pdf	txt/iajs-1204.txt