Allied Journal of Environmental Earth Sciences

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Allied Journal of Environmental Earth Sciences 44 7897 074717

Topology-Top-Journals

 

Topology considers the geometrical properties of a object which are preserved under continuous deformations, like twisting, stretching, crumpling and bending, but not tearing or gluing.

A mathematical space may be a set comprises of a structure, which is called a topology, which allows defining continuous deformation of subspaces, and, more generally, all types of continuity. Euclidean spaces, and, more generally, metric spaces are samples of a mathematical space, as any distance or metric defines a topology. The deformations which are considered in topology are homotopies and homeomorphisms. A property that's invariant under such deformations may be a property of topology. Basic samples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles.

Topology is employed in many branches of mathematics, like differentiable equations, dynamical systems, knot theory, and Riemann surfaces in complex analysis. It is also utilized in string theory in physics, and for describing the space-time structure of universe.

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