Complete lattice: Unit Interval

Complete lattice: Unit Interval
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.

In mathematical analysis, the unit interval is a one-dimensional analytical manifold whose boundary consists of the two points 0 and 1. Its standard orientation goes from 0 to 1.

The unit interval is a totally ordered set and a complete lattice (every subset of the unit interval has a supremum and an infimum).

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