In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points).
[2][3] A topological space is sometimes said to exhibit a property locally, if the property is exhibited "near" each point in one of the following ways: Here, note that condition (2) is for the most part stronger than condition (1), and that extra caution should be taken to distinguish between the two.
For example, some variation in the definition of locally compact can arise as a result of the different choices of these conditions.
A small enough observer standing on the surface of a sphere (e.g., a person and the Earth) would find it indistinguishable from a plane.
Global and local properties formed a significant portion of the early work on the classification of finite simple groups, which was carried out during the 1960s.