Let A x R x is and ocxce Is A lowed Why SolutionSolution G

Let A = {x R x is and ocxce Is A lowed ? Why

Solution

Solution: Given A = { x belongs to R such that x is rational and 0< x <e}

Here A is closed, since every neighbourhood N_x of an element x of A is an open interval

which contains rational and irrational numbers, contains an element of A other than x.

So every element of A is a limit point of A.

Hence A contains all its limit points and hence closed.