One-dimensional space
Introduction The number lineA '''one-dimensional space''' ('''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 algebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more specific terms. Any field  is a one-dimensional vector space over itself. The projective line over  denoted  is a one-dimensional space. In particular, if the field is the complex numbers  then the complex projective line  is one-dimensional with respect to  (but is sometimes called the Riemann sphere, as it is a model of the sphere, two-dimensional with respect to real-number coordinates).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''.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.More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.
Coordinate systems in one-dimensional space One dimensional coordinate systems include the number line.Image:Coord NumberLine.svg|Number line
See also *Univariate*Zero-dimensional space
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