![Euler`s Formula Worksheet 1. Find the](http://s1.studyres.com/store/data/015947725_1-3ed5d806328b5b53e019700fada361c0-300x300.png)
co-γ-Compact Generalized Topologies and c
... which is a subfamily of gγ . Then we show that ϕ need not be a generalized topology on X by the following example. E x a m p l e 3.1. Let X = {a, b, c} , τ = {X, ∅, {a} , {b} , {a, b}} and γ : exp X −→ exp X, γ = ci with the operations i = intτ and c = clτ . Then γ ∈ Γ013 by Theorem 1.11 and Proposi ...
... which is a subfamily of gγ . Then we show that ϕ need not be a generalized topology on X by the following example. E x a m p l e 3.1. Let X = {a, b, c} , τ = {X, ∅, {a} , {b} , {a, b}} and γ : exp X −→ exp X, γ = ci with the operations i = intτ and c = clτ . Then γ ∈ Γ013 by Theorem 1.11 and Proposi ...
An Algorithm to Generate Repeating Hyperbolic Patterns
... fundamental polygon, and with some minimally labeled 2 and 3, and some polygons adjacent to A. exposed and maximally exposed polygons marked with m and M respectively. To describe the replication algorithm, we define the exposure of a polygon by its relation to the next layer. In Figure 7, we say th ...
... fundamental polygon, and with some minimally labeled 2 and 3, and some polygons adjacent to A. exposed and maximally exposed polygons marked with m and M respectively. To describe the replication algorithm, we define the exposure of a polygon by its relation to the next layer. In Figure 7, we say th ...
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.