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

Abstract

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 π-system with “zero” and “unit”) are investigated. Under equipment with topology of Wallman type, the set of MLS is converted into a supercompact T1-space. Conditions under which given space of MLS is a supercompactum (i.e., a supercompact T2-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.