Editing Unit interval (section)

== Generalizations ==
The interval {{closed-closed|-1,1}}, with length two, demarcated by the positive and negative units, occurs frequently, such as in the [[range of a function|range]] of the [[trigonometric function]]s sine and cosine and the [[hyperbolic function]] tanh. This interval may be used for the [[domain of a function|domain]] of [[inverse function]]s. For instance, when {{theta}} is restricted to {{closed-closed|&minus;π/2, π/2}} then <math>\sin\theta</math> is in this interval and arcsine is defined there.

Sometimes, the term "unit interval" is used to refer to objects that play a role in various branches of mathematics analogous to the role that {{closed-closed|0,1}} plays in homotopy theory.  For example, in the theory of [[quiver (mathematics)|quiver]]s, the (analogue of the) unit interval is the graph whose vertex set is <math>\{0,1\}</math> and which contains a single edge ''e'' whose source is 0 and whose target is 1.  One can then define a notion of [[homotopy]] between quiver [[homomorphism]]s analogous to the notion of homotopy between [[continuous function (topology)|continuous]] maps.