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An ambient space or ambient configuration space is the space surrounding an object.

While the ambient space and hodological space are both considered ways of perceiving penetrable space, the former perceives space as navigable while the latter perceives it as navigated.[1]

MathematicsEdit

 
Three examples of different geometries: Euclidean, elliptical, and hyperbolic geometry

In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object along with the object itself. For example, a 1-dimensional line   may be studied in isolation —in which case the ambient space of   is  , or it may be studied as an object embedded in 2-dimensional Euclidean space  —in which case the ambient space of   is  , or as an object embedded in 2-dimensional hyperbolic space  —in which case the ambient space of   is  . To see why this makes a difference, consider the statement "Parallel lines never intersect." This is true if the ambient space is  , but false if the ambient space is  , because the geometric properties of   are different from the geometric properties of  . All spaces are subsets of their ambient space.

See alsoEdit

ReferencesEdit

  1. ^ McMurtrie, Robert James (2017). The Semiotics of Movement in Space. New York: Routledge. p. 41. ISBN 9781138191716.

Further readingEdit