![Some new separation axioms via $\beta$-$\mathcal{I}$](http://s1.studyres.com/store/data/003209001_1-38a56c8ce38255370a67ec3cc0313d7c-300x300.png)
Chapter 9 - SchoolNotes.com
... Theorem: Opposite sides of a parallelogram are congruent. Theorem: Opposite angles of a parallelogram are congruent. Theorem: The diagonals of a parallelogram bisect each other. Theorem: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segm ...
... Theorem: Opposite sides of a parallelogram are congruent. Theorem: Opposite angles of a parallelogram are congruent. Theorem: The diagonals of a parallelogram bisect each other. Theorem: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segm ...
219 PROPERTIES OF (γ,γ )-SEMIOPEN SETS C. Carpintero N
... connected set containing x that is, a (γ, γ 0 )-semi-θ-component of X. Uniqueness of the (γ, γ 0 )-semi-θ-component (containing x) is obvious. (2). Follows from (1). (3). By construction in (1), any (γ, γ 0 )-semi-θ-connected set is contained in the (γ, γ 0 )-semi-θ-component which contains any one ...
... connected set containing x that is, a (γ, γ 0 )-semi-θ-component of X. Uniqueness of the (γ, γ 0 )-semi-θ-component (containing x) is obvious. (2). Follows from (1). (3). By construction in (1), any (γ, γ 0 )-semi-θ-connected set is contained in the (γ, γ 0 )-semi-θ-component which contains any one ...
Notes 8.5 - NOHS Teachers
... THEOREM 8.3: SIDE-ANGLE-SIDE (SAS) SIMILARITY THEOREM If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. ZX XY If aX c aM and , PM MN then T XYZ S T MNP . ...
... THEOREM 8.3: SIDE-ANGLE-SIDE (SAS) SIMILARITY THEOREM If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. ZX XY If aX c aM and , PM MN then T XYZ S T MNP . ...
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.