Let T be an element of B[0,1] be the set V=[B[0,1];f(1)=2]. Prove that T is closed (in metric space B[0,1]). I am not sure if it is obvious since I am new to this stuff but B[0,1] is an open ball I believe. My question is how do I find the complement of V. If I could define B/T then I am hoping it will follow easily from the definitions of open set that this is an open set and my proof will be complete. Is B/T=[B[0,1]; f(1)>2 V f(1)<2]? Very confused.