Some Representations Connected With Ultrafilters and Maximal Linked Systems

Abstract

Ultrafilters and maximal linked systems (MLS) of a lattice of sets are considered. Two following variants of topological equipment are investigated: the Stone and Wallman topologies. These two variants are used both in the case of ultrafilters and for space of MLS. Under Wallman equipment, an analog of superextension is realized. Namely, the space of MLS with topology of the Wallman type is supercompact topological space. By two above-mentioned equipments a bitopological space is realized.

Products of Ultrafilters and Maximal Linked Systems on Widely Understood Measurable Spaces

“…More detailed information on the properties of MLSs can be found in [5][6][7][9][10][11][12]. Now we introduce some constructions for a Stone-type topology.…”

To a Question on the Supercompactness of Ultrafilter Spaces

“…are two bitopological spaces. General properties of these two bitopological spaces are given in [12,13,16].…”

“…In [10], for superextension constructions, a natural bitopological equipping was realized. In the author's consequent papers [11][12][13][14], this approach of [10] was extended to the case when a π-system is used as an anticipating measurable structure (the approach of [6][7][8] corresponds to the case when this π-system is the lattice of closed sets in a T 1 -space). Thus, in the above-mentioned general case of an arbitrary π-system, bitopological spaces of ultrafilters and maximal linked systems were constructed (see [11][12][13][14]).…”