so I'm trying to prove the set $\Omega := \{\varnothing\}\cup\{[0,\infty) \in \mathbb{R}\}\cup\{(a,\infty):a\in\mathbb{R}_{0+}\}$ is a topology on $X=[0, \infty)$, and I'm doing the condition $\forall \Omega_a, \Omega_b$ in $\Omega$, we have $\Omega_a \cup \Omega_b \subset \Omega$.
Let $X$ be the ray $[0, \infty) \subset \mathbb{R}$, and let $\Omega$ consist of $\varnothing$, $X$, and all rays $(a, \infty) \subset \mathbb{R}_{0+}$. I'm trying to prove $\Omega$ is a topology on $X$, but I'm stuck at the idea of an arbitrary subcollection of sets for the proof that an arbitra...
