Exercises
[22Y] Prerequisites:[06M],[06X],[0FR],[21J],[234].Suppose \(H⊆ J\) is cofinal and let \(h={f}_{|{H}}\) be the subnet (as defined in [230]);
Suppose that \(\lim _{j∈ J}f(j)=l∈ \overlineℝ\) show that \(\lim _{j∈ H}h(j)=l\).
Similarly if \((H,\le _ H)\) is cofinal in \((J,\le )\) by means of a map \(i:H\to J\), and \(h=f \circ i\).