Universal specialization semilattices

A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ topological space, $ x y$ means $x \subseteq Ky$, for $x,y X$, and $K$ closure in $X$. Specialization semilattices posets appear as auxiliary structures many disparate scientific fields, even unrelated to topology. In general, not expressible semilattice. On the other hand, we show that every canonically "principal" actually defined.