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Path (topology)
In mathematics, a path in a topological space X is a continuous function from the closed unit interval , 1/math> into X. Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into path-connected components. The set of path-connected components of a space X is often denoted \pi_0(X). One can also define paths and loops in pointed spaces, which are important in homotopy theory. If X is a topological space with basepoint x_0, then a path in X is one whose initial point is x_0. Likewise, a loop in X is one that is based at x_0. Definition A ''curve'' in a topological space X is a continuous function f : J \to X from a non-empty and non-degenerate interval J \subseteq \R. A in X is a curve f : , b\to X whose domain , b/math> is a compact non-degenerate interval (meaning a is homeomorphic to , 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path
A path is a route for physical travel – see Trail. Path or PATH may also refer to: Physical paths of different types * Bicycle path * Bridle path, used by people on horseback * Course (navigation), the intended path of a vehicle * Desire path, created by human or animal foot traffic * Footpath, intended for use only by pedestrians * Shared-use path, intended for multiple modes such as walking, bicycling, in-line skating or others * Sidewalk, a paved path along the side of a road * Hoggin, a buff-coloured gravel & clay pathway often seen in gardens of Stately Homes, Parks etc. * Trail, an unpaved lane or road Mathematics, physics, and computing * Path (computing), in file systems, the human-readable address of a resource ** PATH (variable), in computing, a way to specify a list of directories containing executable programs * Path (graph theory), a sequence of edges of a graph that form a trail ** st-connectivity problem, sometimes known as the "path problem" * Path (topol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |