I would like to consult with anyone who is reading this post on how do you explain the distinction between compact spaces and locally compact spaces to students who had just completed topology course and is now in functional analysis class. In topology, the syllabus cover only Compact spaces and in Functional analysis class, the students were being approach to locally compact spaces.
I can't explain very well and I just say that for locally compact spaces, it is like a subset of a set where the set is a compact spaces. In other words it is a more specific as compared to compact spaces and I don't feel my response is quite clear. Hope to seek some help on the explanation. Thank You.