manifold (redirected from Abstract manifold)

manifold

In mathematics, a topological space (see topology) with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical dynamics. They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations. See also tensor analysis.

---

manifold Formal

1. a chamber or pipe with a number of inlets or outlets used to collect or distribute a fluid. In an internal-combustion engine the inlet manifold carries the vaporized fuel from the carburettor to the inlet ports and the exhaust manifold carries the exhaust gases away

2. Maths

a. a collection of objects or a set

b. a topological space having specific properties

3. (in the philosophy of Kant) the totality of the separate elements of sensation which are then organized by the active mind and conceptualized as a perception of an external object

---

manifold [′man·ə‚fōld]

(engineering)

The branch pipe arrangement which connects the valve parts of a multicylinder engine to a single carburetor or to a muffler.

(mathematics)

A topological space which is locally euclidean; there are four types: topological, piecewise linear, differentiable, and complex, depending on whether the local coordinate systems are obtained from continuous, piecewise linear, differentiable, or complex analytic functions of those in euclidean space; intuitively, a surface.