TOPICS

# Projective Space

Projective space is the generalization of the projective plane to more than two dimensions.

Projective space is a college-level concept that would be first encountered in a topology course.

### Prerequisites

 Euclidean Space: Euclidean space of dimension n is the space of all n-tuples of real numbers which generalizes the two-dimensional plane and three-dimensional space. Projective Plane: The projective plane is the set of lines in the Euclidean plane that pass through the origin. It can also be viewed as the Euclidean plane together with a line at infinity. Topological Space: A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set. Topology: (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties.