1. Chapter 3: Convexity

2. What is Convexity?
A term used in various branches of mathematics and indicating properties which generalize some properties of convex sets
The applicability of a number of methods of study is connected with the term "convexity" .

3. Basic Concepts of Convex
The study of convexity is one of the modern developments that has revitalized Euclidean Geometry.
The study of convex sets employs many ideas of modern mathematics to provide added meaning to concepts that have long been a part of geometry.

4. Basic Concepts
The words “ convex” and “ Convexity” are common outside of mathematics.
Convex means curving outward.
It is describe particular sets of points in mathematics is only a carful retinement of this common meaning.

5. Convex sets

8. Is the Intersection of Two Convex Sets are Convex?

10. If the intersection is empty, or consists of a single point, it is true by definition.
Otherwise, take any points A,B, in the intersection. The line B joining these points must also lie wholly within their intersection
Therefore, the intersection is a convex set.
The intersection of any number of convex sets is also convex.

12. Special Case
An empty set and a single point set are both convex.