id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4581	Boonpok, Chawalit; Khampakdee, Jeeranunt	Upper and Lower Almost Contra-(Λ, sp)-continuity	2023	13	.pdf	application/pdf	5405	374	84	A topological space (X, τ) is called strongly s(Λ, sp)-regular if, for each s(Λ, sp)-closed set K and each x ∈ X −K, there exists a r(Λ, sp)-closed set F containing x such that F ∩K = ∅. Lemma 6. For a multifunction F : (X, τ) → (Y, σ), the following properties are equiv- alent: (1) F is upper almost contra-(Λ, sp)-continuous; (2) F+(K) is (Λ, sp)-open in X for every r(Λ, sp)-closed set K of Y ; (3) F−(V ) is (Λ, sp)-closed in X for every r(Λ, sp)-open set V of Y ; (4) F−([V (Λ,sp)](Λ,sp)) is (Λ, sp)-closed in X for every (Λ, sp)-open set V of Y ; (5) F+([K(Λ,sp)] (Λ,sp)) is (Λ, sp)-open in X for every (Λ, sp)-closed set K of Y ; (6) for each x ∈ X and for each s(Λ, sp)-open set V of Y with F (x) ⊆ V , there exists a (Λ, sp)-open set U of X containing x such that F (U) ⊆ V (Λ,sp); (7) F+(V ) ⊆	cache/ejpam-4581.pdf	txt/ejpam-4581.txt