Give an example of A subset S of R and a proper subset T of

Give an example of

A subset S of R and a proper subset T of S which is closed in the subspace S but not closed in R. T = S =

Solution

S=Set of all Integers.

T_S={x in(1,3)|x in S}={2}

T is closed in S.

T_R ={x in (1,3),x in R}

T_R is open. There are infinite number of real between (1,3).