# Funcoids and reloids, a Galois connection

I proved that $(\mathsf{FCD})$ is the lower adjoint of $(\mathsf{RLD})_{\mathrm{in}}$.

Also from this follows that $(\mathsf{FCD})$ preserves all suprema and $(\mathsf{RLD})_{\mathrm{in}}$ preserves all infima.

See Algebraic General Topology and specifically Funcoids and Reloids online article.