Sentence examples for by a rectifiable path from inspiring English sources

A metric space is said to be rectifiably pathwise connected if each two points of X can be joined by a rectifiable path.

Let ( X, d ) be a complete metric space, and suppose each two points of X can be joined by a rectifiable path.

Let ( X, d ) be a complete metric space for which each two points can be joined by a rectifiable path, and suppose g : X → X is a local radial contraction.

A metric space ( X, d ) is said to be a length space if any two points of X are joined by a rectifiable path (that is, a path of finite length) and the distance between any two points of X is taken to be the infimum of the lengths of all rectifiable paths joining them.

Theorem 2.7 Let X be a complete metric space for which each two points can be joined by a rectifiable path, and suppose g : X → X is a mapping for which g N is a local radial contraction for some N ∈ N. Then g has a unique fixed point x 0, and lim n → ∞ g n ( x ) = x 0 for each x ∈ X.

A metric space ( M, d ) is said to be a length space if each two points of M are joined by a rectifiable path (that is, a path of finite length) and the distance between any two points is taken to be the infimum of the lengh of all rectifiable paths joining them.

Recall that a rectifiable path is a path of finite length (see, e.g., [[5], p.34]).

In case no rectifiable path joins two points of the space, the distance between them is taken to be ∞.

In the case that there is no rectifiable path joins two points of the space, the distance between them is said to be ∞.

In the case that no rectifiable path joins two points of the space, the distance between them is taken to be ∞.

In a global NPC space, each pair of points can be connected by a geodesic (i.e., by a rectifiable curve such that the length of is for all. Moreover, this geodesic is unique. The point that appears in Definition 1.1 is the midpoint of and and has the property. (1.2).