Category:Characterization of Locale

This category contains pages concerning Characterization of Locale:

Let $L = \struct{S, \preceq}$ be an ordered set.

The following statements are equivalent:

$(1)\quad L$ is a locale

$(2)\quad L$ is a frame

$(3)\quad L$ is a complete lattice satisfying the infinite join distributive law

$(4)\quad L$ is a complete Heyting algebra

$(5)\quad L$ is a complete Brouwerian lattice