Tail topology on the natural numbers
= Tail topology on the natural numbers
{title2=$\tau=\{\varnothing\}\cup\{\{n,n+1,\ldots\}:n\in\mathbb N\}$}
The nonempty open sets are the upper tails of the <natural numbers>. Arbitrary nonempty unions select the smallest starting index, and finite intersections select the largest, so these sets form a <topology>. A map into this space is <continuous> exactly when the inverse image of every upper tail is open.