In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with …

Feb 14, 2026 · The basic example of a manifold is Euclidean space, and many of its properties carry over to manifolds. In addition, any smooth boundary of a subset of Euclidean space, like the circle …

Nov 3, 2025 · The term “manifold” comes from Riemann’s Mannigfaltigkeit, which is German for “variety” or “multiplicity.” A manifold is a space that looks Euclidean when you zoom in on any one of …

Manifold, in mathematics, a generalization and abstraction of the notion of a curved surface; a manifold is a topological space that is modeled closely on Euclidean space locally but may vary …

overlaps are Ck-maps with Ck inverses. If we only require the overlap maps to be homeomorphisms we arrive a the notion of a topological manifold. In some very important work of Sullivan one consider L …

lways a one-dimensional manifold. You can have two-dimensional manifolds in the plane R , but they are relatively boring. Examples are: an arbitrary open subset of R2, such as an open square, or a clo

The meaning of MANIFOLD is marked by diversity or variety. How to use manifold in a sentence.

MANIFOLD definition: of many kinds; numerous and varied. See examples of manifold used in a sentence.

1. Many and varied; of many kinds; multiple: our manifold failings. 2. Having many features or forms: manifold intelligence. 3. Being such for a variety of reasons: a manifold traitor. 4. Consisting of or …

Our organization’s problems are manifold – too few members, too little money, and poor management.