What are the properties of topology in point-set topology?

Answer 1

In point-set topology, the properties of the set S are:

• X and ∅ belongs to the set S.
• The intersection of any subsets belongs to the set S.
• The union of any subsets belongs to the set S.

For instance:

Let τ = {X,∅}. Then, it's the topology. We call that the trivial or discrete topology. If the set is indiscrete topology, then it contains infinitely many elements!