Closed unit interval
This article is about a particular topological space (uniquely determined up to homeomorphism)|View a complete list of particular topological spaces
As a subset of the real numbers
The closed unit interval is defined as the interval or the set . It can also be defined as the closed disk with center and radius , i.e., the set:
As a metric space
The closed unit interval is the metric space with the Euclidean metric.
As a manifold with boundary
Fill this in later
As a topological space
The closed unit interval is the set with the subspace topology induced from the real line.
|Space||How strongly is it equivalent to the closed unit interval?|
|for||equivalent as a metric space; in fact, equivalent as a subset of the metric space , in the sense that an isometry of (translation) sends to|
|for ,||equivalent as a (differential) manifold with boundary and hence also as a topological space. Conformally equivalent as a metric space or as a Riemannian manifold with boundary.|
|Two-point compatification of real line, with points introduced at and||equivalent as a (differential) manifold with boundary and hence also as a topological space.|
|Any compact 1-manifold with boundary||equivalent as a (differential) manifold with boundary.|
|Any contractible space||homotopy-equivalent|