Conjecture - Angelfire
... If two lines form right angles, they divide the plane in four equal angles. (True statement) If two lines are perpendicular they divide the plane in four right angles. (Application of the law of Syllogism) ...
... If two lines form right angles, they divide the plane in four equal angles. (True statement) If two lines are perpendicular they divide the plane in four right angles. (Application of the law of Syllogism) ...
COUNTABLE PRODUCTS 1. The Cantor Set Let us constract a very
... Turning again to the Cantor Set G, it should be clear that an element of [0, 1] is in G if ...
... Turning again to the Cantor Set G, it should be clear that an element of [0, 1] is in G if ...
1. (a) Let X be a topological space and γ 0,γ1 : [0
... A subset A of Rn is star-convex if there is a0 ∈ A such that all the line segments joining a0 to other points of A lie in A. Show that a star-convex set is contractible. ...
... A subset A of Rn is star-convex if there is a0 ∈ A such that all the line segments joining a0 to other points of A lie in A. Show that a star-convex set is contractible. ...
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.