# 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:

- The empty set and
*X*are elements of*T*. - The union of any collection of elements in
*T*is in*T*. - The intersection of any finite collection of elements in
*T*is in*T*.

Elements in *T* are called "open sets".