Circle
After a line, a circle is the simplest example of a topological manifold. Topology ignores … See more

Informally, a manifold is a space that is "modeled on" Euclidean space.
There are many different kinds of manifolds. In 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 boundary of an $${\displaystyle n}$$-manifold … See more

The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra 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 single manifold can be constructed in different ways, each stressing a different aspect of the manifold, thereby leading to a slightly different … See more

Topological manifolds
The simplest kind of manifold to define is the topological manifold, which looks locally like some "ordinary" Euclidean space See more