There are many functions to work with regions. For your 1-D example:
alist = Range[0, 1, 0.1];
iv1 = Interval[{Min@alist, Max@alist}] // Chop;
RegionQ[iv1]
True
IntervalMemberQ[iv1, 0.23]
True
You can modify/alter the question with an example that is more useful to you. I will either modify this answer, if I can participate or remove this one.