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In The Elements, Euclid defines a point as that which has no part.
In a vector space, an affine space, or, more generally, an incidence geometry, a point is a zero dimensional object.
In a projective geometry, a point is a one-dimensional subspace of the vector space underlying the projective geometry.
In a topology, a point is an element of a topological space.
In function theory, a point usually means a complex number as an element of the complex plane.
Note that there is also the possibility for a point-free approach to geometry in which points are not assumed as a primitive. Instead, points are defined by suitable abstraction processes. (See point-free geometry.)
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"point" is owned by Wkbj79. [ full author list (4) ]
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Cross-references: point-free geometry, primitive, geometry, complex plane, complex number, function theory, element, topology, subspace, projective geometry, incidence geometry, affine space, vector space
There are 1389 references to this entry.
This is version 13 of point, born on 2006-07-24, modified 2010-07-14.
Object id is 8173, canonical name is Point.
Accessed 14465 times total.
Classification:
| AMS MSC: | 51-00 (Geometry :: General reference works ) | | | 54-00 (General topology :: General reference works ) | | | 15-00 (Linear and multilinear algebra; matrix theory :: General reference works ) |
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Pending Errata and Addenda
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