Definition

Let ''X'' be a subset of R^''n''. Then reach of ''X'' is defined as :

\text(X) := 
    \sup \.

Examples

Shapes that have reach infinity include * a single point, * a straight line, * a full square, and * any

convex set In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex ...

. The graph of ''ƒ''(''x'') = , ''x'', has reach zero. A circle of radius ''r'' has reach ''r''.

References

* {{citation , last = Federer , first = Herbert , authorlink = Herbert Federer , title = Geometric measure theory , publisher = Springer-Verlag New York Inc. , location = New York , year = 1969 , pages = xiv+676 , isbn = 978-3-540-60656-7 , zbl=0176.00801 , mr=0257325 , series = Die Grundlehren der mathematischen Wissenschaften , volume = 153 Geometric measurement Real analysis Topology