# Is there a name for an order topology in which every base interval is non-empty?

Is there a name for an order topology $\tau$ over a totally ordered set $X$ that satisfies the following condition: for every $a, b \in X\cup\{\pm\infty\}$ if $a < b$, then $(a,b) \neq \emptyset$?

An order dense LOTS (linearly ordered topological space, see Wikipedia, e.g. ) without maximum or mininum. $\mathbb{Q}$ is the only such countable linear order, up to isomorphism. The absence of a minimum or maximum could be called "unbounded", I suppose. So "an unbounded order-dense LOTS"?