Please explain more about what you need. Did you intend to write t[t2, t3] with the t at the beginning? Are those ordered pairs or something? Is there any ordering or sorting of the pair in the data structure?

Thank you for your answer.
Well, I think that a good example may be given by wave function. Let's assume that t is time, so that you have a natural sorting defined
on t values. In a such scenario, f(t) may assume two distinct values, 1 or 0, in different time intervals like [t1,t2] and [t3,t4]..
Let's assume that f(t) assumes 1 as value when a certain system is doing calculations, and 0 when that system is idle. I want to answer to questions like these:
- from a certain time t, for how may minutes system has been up ?
- form a certain time t, has been the system up for at least T minutes ?