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    Topological Space

    Basic definition

    A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set.

    Detailed definition

    A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 
1. The empty set ∅ is in T. 
2.X is in T. 
3. The intersection of a finite number of sets in T is also in T. 
4. The union of an arbitrary number of sets in T is also in T. 
Alternatively, T may be defined to be the closed sets rather than the open sets, in which case conditions 3 and 4 become: 
3. The intersection of an arbitrary number of sets in T is also in T.

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