What would you like to understand?

A topological space is written as the ordered pair (X, τ) because the same underlying set X can carry different topologies. The topology τ specifies which subsets of X are considered open, so the structure of the space depends on both the set and the chosen collection of open subsets.

Conditions: X is a set.; τ is a topology on X.

A topological space is written as the ordered pair (X, τ) because the same underlying set X can carry different topologies. The topology τ specifies which subsets of X are considered open, so the structure of the space depends on both the set and the chosen collection of open subsets.

Conditions: X is a set.; τ is a topology on X.