One-dimensional space

[1] Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded.

Examples include the circle on a plane, or a parametric space curve.

In physical space, a 1D subspace is called a "linear dimension" (rectilinear or curvilinear), with units of length (e.g., metre).

In algebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more specific terms.

For every eigenvector of a linear transformation T on a vector space V, there is a one-dimensional space A ⊂ V generated by the eigenvector such that T(A) = A, that is, A is an invariant set under the action of T.[2] In Lie theory, a one-dimensional subspace of a Lie algebra is mapped to a one-parameter group under the Lie group–Lie algebra correspondence.

One dimensional coordinate systems include the number line.