I have a little doubt about use if article before the word open. Which one is correct in the following examples: There exists an open interval. There exists a open interval. What is the rule?
Which to use depends on whether the following word starts with a vowel sound. "University" start with the y-consonant sound, so it's "a university", but "hour" starts with a vowel sound, so an "an hour". Interval also starts with a vowel sound, so it is "an interval".
If "university" were pronounced with an 'oo' sound, rather than a 'yoo' sound, it would use "an" as well.