A vector bundle is a family of vector spaces parametrized continuously by a topological space X. More precisely, a vector bundle over X is a topological space E equipped with a continuous map π π : E → → X such that for every x in X, the fiber π (x) is a vector space. The case dim V = 1 is called a line bundle. For any vector space V, the projection X × V → X makes the product X × V into a "trivial" vector bundle. Vector bundles over X are required to be locally a product of X and some (fixed) vector space V : for every x in X, there is a neighborhood U of x such that the restriction of π to π (U) is isomorphic to the trivial bundle U × V → U. Despite their locally trivial character, vector bundles may (depending on the shape of the underlying space X) be "twisted" in the large (that is, the bundle need not be (globally isomorphic to) the trivial bundle X × V). For example, the Möbius strip can be seen as a line bundle over the circle S (by identifying open intervals with the real line). It is, however, different from the cylinder S × R, because the latter is orientable whereas the former is not.