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Topology : Subspace

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Suppose (X,T) is a topological space. Let Y be non-empty subset of X. The the set J={intersection(Y,U) : U is in T} is called the subspace toplogy on Y. Prove that J indeed a toplogy on Y i.e., (Y,J) is a topological space.

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Solution Summary

Topological subspaces are investigated. The solution is detailed and well presented.