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An open interval is an interval that does not include its end points. The open interval {x:a<x<b} is denoted (a,b), although the nonstandard notation ]a,b[ is sometimes also ...

The four of Hilbert's axioms which concern the arrangement of points.

The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described ...

In the above figure, the sides a and b have the same length, appearances to the contrary. In the related illusion illustrated above, the interior lines appear to be of ...

If (X,x) and (Y,y) are pointed spaces, a pointed map is a continuous map F:X->Y with the additional requirement that F(x)=y.

A pointed space is a topological space X together with a choice of a basepoint x in X. The notation for a pointed space is (X,x). Maps between two pointed spaces must take ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

A word derived from the Latin roots quad- (four) and via (ways, roads), therefore a crossing of four roads. In medieval universities, the quadrivium consisted of the four ...

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...