I have the topologies given in 2 answers here [Putting a topology on the disjoint union and what are the open sets.](https://math.stackexchange.com/questions/3518250/putting-a-topology-on-the-disjoint-union-and-what-are-the-open-sets?noredirect=1#comment7244798_3518250) but actually I am unable to show that either one of them is a topology. could anyone help me in doing so please?