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A closed curve is thus the image of a continuous mapping of a circle. A non-closed curve may also be called an open curve. If the domain of a topological curve is a closed and bounded interval = [,], the curve is called a path, also known as topological arc (or just arc).
A Jordan curve or a simple closed curve in the plane R 2 is the image C of an injective continuous map of a circle into the plane, φ: S 1 → R 2. A Jordan arc in the plane is the image of an injective continuous map of a closed and bounded interval [a, b] into the plane. It is a plane curve that is not necessarily smooth nor algebraic.
A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall.
This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ...
In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", [3] the authors state: The only type of causality violation that the authors would find unacceptable is that embodied in the science-fiction concept of going backward in time and killing one's younger self ("changing the past").
By the Jordan curve theorem, every closed trajectory divides the plane into two regions, the interior and the exterior of the curve.. Given a limit cycle and a trajectory in its interior that approaches the limit cycle for time approaching +, then there is a neighborhood around the limit cycle such that all trajectories in the interior that start in the neighborhood approach the limit cycle ...
By the Jordan curve theorem, a simple closed curve divides the plane into interior and exterior regions, and another equivalent definition of a closed convex curve is that it is a simple closed curve whose union with its interior is a convex set. [9] [17] Examples of open and unbounded convex curves include the graphs of convex functions.
Definition: A map f : X → Y is called closed if its graph is closed in X × Y. In particular, the term " closed linear operator " will almost certainly refer to a linear map whose graph is closed. Otherwise, especially in literature about point-set topology , " f is closed" may instead mean the following: