In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an $${\displaystyle n}$$-dimensional manifold, or See more

The spherical Earth is navigated using flat maps or charts, collected in an atlas. Similarly, a manifold can be described using See more

A manifold with boundary is a manifold with an edge. For example, a sheet of paper is a 2-manifold with a 1-dimensional boundary. The … See more

The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as … See more

Circle
After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line. Considering, for instance, the top … See more

Informally, a manifold is a space that is "modeled on" Euclidean space.
There are many different kinds of manifolds. In geometry and topology, all manifolds are See more

A single manifold can be constructed in different ways, each stressing a different aspect of the manifold, thereby leading to a slightly different … See more