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Load path analysis is a technique of mechanical and structural engineering used to determine the path of maximum stress in a non-uniform load-bearing member in response to an applied load. Load path analysis can be used to minimize the material needed in the load-bearing member to support the design load. Load path analysis may be performed ...
In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B.
In mathematics, a path in a topological space is a continuous function from a closed interval into . 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 .
Let (Ω, Σ, P) be a probability space.Let X : I × Ω → S be a stochastic process, where the index set I and state space S are both topological spaces.Then the process X is called sample-continuous (or almost surely continuous, or simply continuous) if the map X(ω) : I → S is continuous as a function of topological spaces for P-almost all ω in Ω.
If * is a one-point space then one can identify C(*, Y) with Y, and under this identification the compact-open topology agrees with the topology on Y.More generally, if X is a discrete space, then C(X, Y) can be identified with the cartesian product of |X| copies of Y and the compact-open topology agrees with the product topology.
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. Alternatively, a Jordan curve is the image of a continuous map φ: [0,1] → R 2 such that φ(0) = φ(1) and the restriction of φ to [0,1) is
Continuous track or tracked treads are a system of vehicle propulsion used in tracked vehicles, running on a continuous band of treads or track plates driven by two or more wheels. The large surface area of the tracks distributes the weight of the vehicle better than steel or rubber tyres on an equivalent vehicle, enabling continuous tracked ...
The Hawaiian earring is not semi-locally simply connected.. A simple example of a space that is not semi-locally simply connected is the Hawaiian earring: the union of the circles in the Euclidean plane with centers (1/n, 0) and radii 1/n, for n a natural number.