Some topological properties of the space of maximal linked systems with topology of Wallman type

Maximal linked systems (MLS) and ultrafilters (u/f) on a widely understood measurable space (this is a nonempty set with equipment in the form of $\pi$-system with «zero» and «unit») are investigated. Under equipment with topology of Wallman type, the set of MLS is converted into a supercompact $T_1$-space. Conditions under which given space of MLS is a supercompactum (i. e., a supercompact $T_2$-space) are investigated. These conditions then apply to the space of u/f under equipment with topology of Wallman type. The obtained conditions are coordinated with representations obtained under degenerate cases of bitopological spaces with topologies of Wallman and Stone types, but they are not the last to be exhausted.