id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5320	Khampakdee, Jeeranunt ; Sompong, Supannee ; Boonpok, Chawalit	$c$-$(\tau_1,\tau_2)$-continuity for Multifunctions	2024	11	.pdf	application/pdf	4326	330	73	In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . For a multifunction F : (X, τ1, τ2) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper c-(τ1, τ2)-continuous at x ∈ X; (2) x ∈ τ1τ2-Int(F +(V )) for each σ1σ2-open set V of Y containing F (x) and having σ1σ2-compact complement; (3) x ∈ F−(σ1σ2-Cl(B)) for each subset B of Y having the σ1σ2-compact σ1σ2-closure such that x ∈ τ1τ2-Cl(F −(B)); (4) x ∈ τ1τ2-Int(F +(B)) for each subset B of Y such that Y − σ1σ2-Int(B) is σ1σ2- compact and x ∈ F+(σ1σ2-Int(B)).	cache/ejpam-5320.pdf	txt/ejpam-5320.txt