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(Topology) Prove that the interior of a subset A of Xτ is the union of all...

(Topology) Prove that the interior of a subset A of Xτ is the union of all τ -open sets contained in A.

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Expert Solution

(X,τ) is a topological space and A⊆X then a point a∈A is said to be an interior point of A if there exists an open neighbourhood U of a contained in A, that is, there exists a U∈τ with a∈U such that

a∈U⊆A

We call the set of all interior points of A the interior of A and denoted it by int(A) .

Colby Messinger answered 1 week ago
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