15 the geometry of whales and ants non
... as Earth), the sum of the angles of a triangle is greater than 180 degrees. Rectangles do not exist, but right-angled triangles do. Keep in mind the curvature of the Earth! For example, a triangle can be drawn with three right ...
... as Earth), the sum of the angles of a triangle is greater than 180 degrees. Rectangles do not exist, but right-angled triangles do. Keep in mind the curvature of the Earth! For example, a triangle can be drawn with three right ...
A note on coherence of dcpos - School of Computer Science
... Proof. For every x, y ∈ L the intersection of ↑x and ↑y, which is ↑(x ∨ y), is always compact, so the statement follows from Lemma 3.1. The following fact about core-compact complete lattices is essentially due to G. Gierz and K.H. Hofmann [2]; we collect it here as a corollary to the previous resul ...
... Proof. For every x, y ∈ L the intersection of ↑x and ↑y, which is ↑(x ∨ y), is always compact, so the statement follows from Lemma 3.1. The following fact about core-compact complete lattices is essentially due to G. Gierz and K.H. Hofmann [2]; we collect it here as a corollary to the previous resul ...
Submaximality, Extremal Disconnectedness and Generalized
... α-clS = S Scl(int(clS)) and! ! sclS = S int(clS), pclS = S cl(intS) and spclS = S int(cl(intS)). The α-interior T of S ⊆ X is the largest α-open set contained in S, and we have α-intS = S int(cl(intS)). It is worth mentioning that the collection of all α-open subsets of (X, τ ) is a topology τ α on ...
... α-clS = S Scl(int(clS)) and! ! sclS = S int(clS), pclS = S cl(intS) and spclS = S int(cl(intS)). The α-interior T of S ⊆ X is the largest α-open set contained in S, and we have α-intS = S int(cl(intS)). It is worth mentioning that the collection of all α-open subsets of (X, τ ) is a topology τ α on ...
Non-Hausdorff multifunction generalization of the Kelley
... central among the topological Ascoli theorems for continuous functions on a k -space. It generalizes to the fc3-space theorem of [1], which contains all known Ascoli theorems for k -spaces or fe3-spaces. Obviously a multifunction generalization depends on a multifunction extension of "even continuit ...
... central among the topological Ascoli theorems for continuous functions on a k -space. It generalizes to the fc3-space theorem of [1], which contains all known Ascoli theorems for k -spaces or fe3-spaces. Obviously a multifunction generalization depends on a multifunction extension of "even continuit ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.