In each case \((a)\). (b), (c) below sliow that
(i) \(X=R, H=\\{\emptyset\rfloor(\cup \mid K\\} \cup\\{(\infty, x) ; x \in
R\\}\).
(h) \(\mathrm{X}=\mathrm{N}=\) the positive integers \(=\) the natural numbers,
\(\boldsymbol{u}=\\{\boldsymbol{\theta}\\}\) \(\cup(N\\} \cup\left\\{O_{n}: 11:
1\right)\) where \(O_{n}=\\{n, n+1, n+2, \ldots\\} .\)
(c) \(\mathrm{X}=\mathrm{R}, U \in \mathbb{H}\) if and only if \(\mathrm{G}\) is a
subset of \(\mathrm{R}\) and for each \(\mathrm{s} \in \mathrm{t}\) \\} there is a
\(t>\) s such that |s.t) \(\subseteq U\). where \(\mid s, t)=\\{x \in R: s
