The pushforward of a map, is from this kind of space to this kind of space.
Linear operators which satisfy the Leibnitz rule are equivalent to this type of space for a smooth manifold. One way of constructing this type of space using the dual of the ratio of a maximal ideal and the square of a maximal ideal is named for Zariski. The pushforward of a map, is from this kind of space to this kind of space. Given an affine connection, one can define a geodesic as a curve which parallel transports its own (*) vector of this type. A vector field on a manifold is a map from the manifold to this bundle. This kind of vector is defined as the partial derivative of each vector component with respect to its coordinate. This function is the square root of secant squared minus 1, and the derivative is the slope of a line which has this relationship to a curve. For 10 points, what word names the function which is given by sine over cosine?
Linear operators which satisfy the Leibnitz rule are equivalent to this type of space for a smooth manifold.
tangent [or tangent space or tangent function; or tan]