The situation is different for closed intervals.
In this case H is the indicator function of a closed semi-infinite interval:
Examples include a closed interval or a rectangle.
A closed interval includes its endpoints, and is denoted with square brackets.
Let I be a set of closed intervals of the real line with an empty intersection.
It represents the idea that the graph of a continuous function on a closed interval can be drawn without lifting your pencil from the paper.
That is, on any closed interval of the real line, takes on every value between and .
Indeed takes on the value of every real number on any closed interval where .
A step function on a closed interval is a function of the form:
For example, any closed interval on the real line is unicoherent, but a circle is not.
Wörterbuch für Mathematik