![On products of maximally resolvable spaces](http://s1.studyres.com/store/data/002296580_1-a32448ea09b3e19ec24995a17c96cb37-300x300.png)
CK-12 Geometry: Proving Quadrilaterals are Parallelograms
... Converse, you would have to find the length (using the distance formula) of each side to see if the opposite sides are congruent. To use the Parallelogram Diagonals Converse, you would need to use the midpoint formula for each diagonal to see if the midpoint is the same for both. Finally, you can u ...
... Converse, you would have to find the length (using the distance formula) of each side to see if the opposite sides are congruent. To use the Parallelogram Diagonals Converse, you would need to use the midpoint formula for each diagonal to see if the midpoint is the same for both. Finally, you can u ...
Modern descriptive set theory
... converges to f ∈ C(X, Y ) if and only if for every sequence xn ∈ X : n ∈ ω of points in the space X with limit x ∈ X, and every increasing sequence mn : n ∈ ω of natural numbers it is the case that the points fn (xmn ) : n ∈ ω converge to f (x) in the space Y . Theorem 2.2.9. If X is a compact Polis ...
... converges to f ∈ C(X, Y ) if and only if for every sequence xn ∈ X : n ∈ ω of points in the space X with limit x ∈ X, and every increasing sequence mn : n ∈ ω of natural numbers it is the case that the points fn (xmn ) : n ∈ ω converge to f (x) in the space Y . Theorem 2.2.9. If X is a compact Polis ...
3-manifold
![](https://commons.wikimedia.org/wiki/Special:FilePath/3-Manifold_3-Torus.png?width=300)
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.