We show that if f_i : X_i → Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly θ-continuous, θ-continuous, continuous, V-map), then F : X₁ ◎ X₂ → Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly θ-continuous, θ-continuous, g-continuous, V-map).