# Manifold

A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension.

Manifold is a graduate-level concept that would be first encountered in a topology course.

### Examples

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. |

Möbius Strip: | A Moebius strip is one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving it half a twist, and then reattaching the two ends. |

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. |

Sphere: | A sphere is the set of all points in three-dimensional space that are located at a fixed distance from a given point. |

Torus: | A torus is a closed surface containing a single hole that is shaped like a doughnut. |

### Prerequisites

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. |