Sentence examples for map with closed from inspiring English sources

map with closed values, then is closed.

Then, for an arbitrary neighborhood U of 0, there exist a U and b U in A for which b U ∈ T ( a U ) ∩ ( a U + U ). Since T is compact, we conclude that thereis a 0 ∈ T ( A ) ¯ ⊆ A in which the net b U ⟶ a 0. Because X is Hausdorff, a U ⟶ a 0. Since T is an upper semicontinuousset-valued map with closed values, Graph ( T ) is closed.

map with closed ∞-proximally connected values in Y;   (ii) (Psi:Xrightrightarrows X) be a compact l.s.c.

map with closed ∞-proximally connected values in Y; (Psi:Xrightrightarrows X) be a compact l.s.c.

Since G ¯ is a KKM map with closed values, by Theorem 2.7, we have K ∩ ⋂ z ∈ D G ( z ) ¯ ≠ ∅.

Let (Asubset X) be a closed subset and (varphicolonOmegatimes Amultimap X) be a multivalued map with closed values.

If T : A → 2 B is an upper semicontinuous mapping with closed values, then T is closed.

Hence Γ is a KKM mapping with closed values.

By (ii), T is a KKM mapping with closed values.

SFBFP ⇒ KKMP: Let F : X ↦ 2 Y be a KKM mapping with closed values.

Furthermore, suppose (T : X rightrightarrows X ) is a KKM mapping with closed values.