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In mathematics, the unit interval is the closed interval [0,1], that is,
the set of all real numbers that are greater than or equal to 0
and less than or equal to 1.

It is often denoted I (capital letter I). In addition to its role in real analysis,
the unit interval is used to study homotopy theory in the field of topology.

Properties

The unit interval is a complete metric space, homeomorphic to
the extended real number line.
As a topological space, it is compact, contractible, path connected
and locally path connected.
The Hilbert cube is obtained by taking a topological product of
countably many copies of the unit interval.

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