Closed unit interval

As a subset of the real numbers
The closed unit interval is defined as the interval $$[0,1]$$ or the set $$\{ x \in \R \mid 0 \le x \le 1\}$$. It can also be defined as the closed disk with center $$1/2$$ and radius $$1/2$$, i.e., the set:

$$\{ x \in \R \mid |x - 1/2| \le 1/2\}$$

As a metric space
The closed unit interval is the metric space $$[0,1]$$ with the Euclidean metric.

As a topological space
The closed unit interval is the set $$[0,1]$$ with the subspace topology induced from the real line.