Embedding Partially Ordered Spaces in Topological Semilattices
Embedding Partially Ordered Spaces in Topological Semilattices
A partial order $\Gamma$ on a compact space S is called continuous if $\Gamma$ is a closed subset of $S \times S$. In this paper, we define and study an embedding $\Phi$ of the arbitrary compact continuously partially ordered space $(S,\Gamma )$ into a corresponding compact topological semilattice ${S_\Gamma }$. …