total order

A total order is a homogeneous relation that is reflexive, transitive, connected, and antisymmetric.

Formally,
a binary relation $\le$ over a set $S$ is a total order if for all $a,b,c$ in $S$,

• $a\le a$ (reflexive)
• If $a\le b$ and $b\le c$ then $a\le c$ (transitive)
• If $a\le b$ then $b\nleqq a$ (antisymmetric)
• $a\le b$ or $b\le a$ (connected)

A total order is a partial order that is connected.
Or, a weak order that is antisymmetric.