For n ≥ 1, let gn and g be functions defined on E ( Rk into R, and recall that {gn} is said to converge continuously to g on E, if for every x ( E, gn(xn) →g(x) whenever xn →x, as n→∞. Then show that if {gn} converges continuously to g on E, it follows that g is continuous on E.