For the curious --
>> It seems as though including the words "single point" is an
>> assurance that "closed" makes sense as an answer, although I'm
not
>> sure if there are other answers that make sense as well.
I'd say that "measurable" is the best answer that's still correct
after the quoted portion. The phrase "...that includes its
endpoints" would be quite extraneous, in that case, though. You
gotta look pretty hard to find a nonmeasurable set.
One other small thing -- there was some talk earlier of the
classification of countable/finite sets as compact or not. Any
finite set is (rather trivially) compact.
--Nate