Alexander G. Chentsov     (Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation)


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.


Lattice, Linked system, Ultrafilter

Full Text:



de Groot J. Superextensions and supercompactness // Proc. I. Intern. Symp. on extension theory of topological structures and its applications. Berlin: VEB Deutscher Verlag Wis., 1969. P. 89–90.

van Mill J. Supercompactness and Wallman spaces. Amsterdam. Math. Center Tract., 85. 1977.

Strok M. and Szymanski. Compact metric spaces have binary bases // Fund. Math., 1975. Vol. 89. P. 81–91.

Fedorchuk V.V., Filippov V.V. Obshhaya topologiya. Osnovnyie konstrukzii. M.: Fismatlit, 2006. [in Russian]

Chentsov A.G. Ultrafilters and maximal linked systems of sets // Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017. Vol. 27, no. 3. P. 365–388. [in Russian]

Chentsov A.G. Filters and ultrafilters in the constructions of attraction sets // Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011. No. 1, P. 113–142. [in Russian]

Chentsov A.G. Tier mappings and ultrafilter-based transformations // Trudy Inst. Mat. i Mekh. UrO RAN, 2012. Vol. 18, no. 4. P. 298–314. [in Russian]

Chentsov A.G. Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature // Steklov Inst. Math. 2017. Vol. 296, suppl. 1. P. 102–118. DOI: 10.1134/S0081543817020109

Dvalishvili B.P. Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures, and Applications. Nort-Holland. Mathematics studies. 2005.

Kuratowski K., Mostowski A. Set theory. Amserdam: North-Holland, 1967.

Alexanfroff P.S. Vvedenie v teoriyu mnogestv i obshhuju topologiyu. M.: Editorial URSS, 2004. [in Russian]

Alexandroff A.D. Additive set-functions in abstract spaces // Mathematics of the USSR-Sbornik. 1940. Vol. 8, no. 2. P. 307–348.

Engelking R. General topology. Warsaw: PWN. 1977.

Chentsov A.G. Attraction sets in abstract attainability problems: equivalent representations and basic properties // Russ Math., 2013. Vol. 57, no. 28. DOI: 10.3103/S1066369X13110030

Chentsov A.G., Pytkeev E.G. Some topological structures of extensions of abstract reachability problems // Proc. Steklov Inst. Math., 2016. 292, suppl. 1. P. 36–54. DOI: 10.1134/S0081543816020048

Chentsov A.G. Superextension as bitopological space // Izv. IMI UdGU, 2017. Vol. 49. P. 55–79. [in Russian]

Chentsov A.G. To the validity of constraints in the class of generalized elements // Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014. Vol. 3. P. 90–109. [in Russian]


Article Metrics

Metrics Loading ...


  • There are currently no refbacks.