Topological space

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A topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following 3 axioms:

  1. The empty set and X are elements of T.
  2. The union of any collection of elements in T is in T.
  3. The intersection of any finite collection of elements in T is in T.

Elements in T are called "open sets".