= Upper-ray topology on the real line
{title2=$\{\varnothing,\mathbb R\}\cup\{(a,\infty):a\in\mathbb R\}$}
These sets form a <topology>: a nonempty union of upper rays is another upper ray, or all of $\mathbb R$ when their endpoints have no lower bound; a finite intersection of rays has endpoint the maximum of their endpoints. The whole line must be included. The <continuous map> $n\mapsto n$ from $\mathbb N$ with the <cofinite topology> to this space is nonconstant, because each upper ray has cofinite inverse image.
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