Boundary

Boundary (plural: boundaries) may refer to

Political geography

Psychology

Sociology

Mathematics and physics

Other

Boundary (cricket)

In cricket a boundary is the edge or boundary of the playing field, or a scoring shot where the ball is hit to or beyond that point.

Edge of the field

The boundary is the edge of the playing field, or the physical object marking the edge of the field, such as a rope or fence. In low-level matches, a series of plastic cones are often used. Since the early 2000s the boundaries at professional matches are often a series of padded cushions carrying sponsors' logos strung along a rope. If it is moved during play (such as by a fielder sliding into the rope) the boundary is considered to remain at the point where that object first stood.

When the cricket ball is inside the boundary, it is live. When the ball is touching the boundary, grounded beyond the boundary, or being touched by a fielder who is himself either touching the boundary or grounded beyond it, it is dead and the batting side usually scores 4 or 6 runs for hitting the ball over the boundary. Because of this rule, fielders near the boundary attempting to intercept the ball while running or diving, often flick the ball back in to the field of play rather than pick it up directly, because their momentum could carry them beyond the rope while holding the ball. They then return to the field to pick the ball up and throw it back to the bowler.

Topological manifold

In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout mathematics.

A manifold can mean a topological manifold, or more frequently, a topological manifold together with some additional structure. Differentiable manifolds, for example, are topological manifolds equipped with a differential structure. Every manifold has an underlying topological manifold, obtained simply by forgetting the additional structure. An overview of the manifold concept is given in that article. This article focuses purely on the topological aspects of manifolds.

Formal definition

A topological space X is called locally Euclidean if there is a non-negative integer n such that every point in X has a neighborhood which is homeomorphic to the Euclidean space Eⁿ (or, equivalently, to the real n-space Rⁿ, or to some connected open subset of either of two).