One-dimensional space

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A one-dimensional (1D) space is a mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real number. 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. Any field K is a one-dimensional vector space over itself. The projective line over K, denoted 𝐏1(K), is a one-dimensional space. In particular, if the field is the complex numbers ℂ, then the complex projective line 𝐏1(ℂ) is one-dimensional with respect to ℂ (but is sometimes called the Riemann sphere, as it is...

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