2. Let X be a topological space. Then the empty set and X are sets that are both open and closed!
Open and Closed Sets have got nothing to do with the day-to-day open and closed.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda