Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
If (X,T) is disconnected, then there exists a separation (U,V), where U and V are disjoint open non-empty subsets of (X,T) Since we are given T ⊂ T', then U and V are open non-empty subsets of (X,T'), and their union is X. Then, (U,V) is a separation of (X,T'), so (X,T') is disconnected. Conversely, if (X,T') is connected, then (X,T) is connected.