# 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. |