In the literature, the term "unit interval" is also sometimes applied to the other shapes that an interval from 0 to 1 could take, that is (0,1], [0,1), and (0,1). However, it's most commonly reserved for the closed interval [0,1], and Wikipedia follows this convention.
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 [0,1] plays in homotopy theory. For example, in the theory of quivers, the (analogue of the) unit interval is the graph whose vertex set is {0,1} 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 homomorphisms analogous to the notion of homotopy between continuous maps.
In all of its guises, the unit interval is almost always written I, and the following ASCII picture suffices in almost any context:
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0 1
I
In telecommunications, a unit interval is defined as: In isochronous transmission, the longest interval of which the theoretical durations of the significant intervals of a signal are all whole multiples.
Source: Federal Standard 1037C in support of MILSTD188
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