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 … 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 $${\displaystyle \mathbb {R} ^{n}}$$. By definition, all manifolds are topological manifolds, so the … 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 topological manifolds, possibly with additional structure. A manifold can be … 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 and … See more