Let XX bet a subset of RR, and let f:X→Rf:X→R be a continuous function. If YY is a subset of XX, show that the restriction f|Y:Y→Rf|Y:Y→R of ff to YY is also a continuous function.
My attempt
The definition of continuity is, let XX be a subset of RR and let ∗F∗∗F∗ : X→RX→R be a function. Let x0x0 be an element of XX. We say that FF is continuous at x0x0 iff limx→x0;x∈Xlimx→x0;x∈X. After this, I'm not sure how to continue with the proof.