Let (X,3) be a topological space. We define the closure of a subset ACX to be the union of A and the set of limit points

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Let X 3 Be A Topological Space We Define The Closure Of A Subset Acx To Be The Union Of A And The Set Of Limit Points 1 (87.52 KiB) Viewed 41 times

Let (X,3) be a topological space. We define the closure of a subset ACX to be the union of A and the set of limit points of A. The closure is denoted by cl(A). Show that the closure of ACX is the intersection of all closed sets in X containing A. That is, cl(A) = Va, αεΙ where {Va}ael is the collection of closed sets in X containing A.