The axioms formulated by Hausdorff for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood set E of x. 1. There corresponds to each point x at least one neighborhood U(x), and each neighborhood U(x) contains the point x. 2. If U(x) and V(x) are two neighborhoods of the same point x, there must exist a neighborhood W(x) that is a subset of both. 3. If the point y lies in U(x), there must exist a neighborhood U(y) that is a subset of U(x).
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