Point 2006-07-24 20:35:10 2007-01-16 15:57:25 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here In {\sl 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 {\sl point\/} is a \PMlinkname{zero}{Zero} \PMlinkname{dimensional}{Dimension3} \PMlinkescapetext{object}. In a projective geometry, a {\sl point\/} is a one-dimensional subspace of the vector space underlying the projective geometry. In a topology, a {\sl point\/} is an element of a topological space. 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.)