Sentence examples for be a nonempty abstract from inspiring English sources

Let A be a nonempty abstract set.

Let E be a nonempty abstract set.

Let be a nonempty set, an abstract convex space, and a topological space.

Let be a nonempty subset of an abstract convex uniform space which has a uniformity, and has a symmetric basis.

Let (X ⊇ D, Γ) be an abstract convex space, Y be a nonempty set and f be a real-valued bifunction defined on X × Y. Then f is said to be (1) quasi-abstract convex in the first variable if, for all y ∈ Y and γ ∈ ℝ, the set (x ∈ X : f x, y) < γ} is abstract convex.

Let (X, Γ) is an abstract convex space and Y be a nonempty set.

Let be a nonempty set, let be an almost -convex subset of an abstract convex uniform space, let and be two topological spaces, and let be a multifunction.

Let be a nonempty set, let be an almost -convex subset of an abstract convex uniform space which has a uniformity and has a symmetric basis, and let be a topological space.

In the rest of this paper, let ((X,Gamma)) be an abstract convex Hausdorff topological space and E be a nonempty compact subset of X.

Let Y be a nonempty set, Z be a minimal space, s : Y → D be a function and (X, D, Γ) be an abstract convex space.

The only substantive requirement introduced by (5) is that there be a nonempty positive analogy.