id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-7050	Thongmoon, Montri ; Sama-Ae, Areeyuth ; Boonpok, Chawalit	On upper and lower weakly $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions	2025	14	.pdf	application/pdf	5585	407	82	A multifunction F : (X, τ,I ) → (Y, σ1, σ2) is said to be upper weakly τ⋆β(σ1, σ2)-continuous if F is upper weakly τ⋆β(σ1, σ2)-continuous at each point of X. Theorem 1. For a multifunction F : (X, τ,I ) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper weakly τ⋆β(σ1, σ2)-continuous at a point x ∈ X; (2) x ∈ Cl⋆(Int(Cl⋆(F+(σ1σ2-Cl(V ))))) for every σ1σ2-open set V of Y containing F (x); (3) x ∈ βInt⋆(F+(σ1σ2-Cl(V ))) for every σ1σ2-open set V of Y containing F (x).	cache/ejpam-7050.pdf	txt/ejpam-7050.txt