nLab
subsingleton

A subsingleton generally refers to a subset (of some ambient set $A$) having at most one element. That is, it is a subset $B$ of $A$ such that any two elements of $B$ are equal.

Of course, classically any subsingleton is either empty or a singleton, but constructively this need not hold. In a topos, the “object of subsingletons in $A$” is the partial map classifier? for $A$, often denoted $A_{\perp }$.