Geodesic
Ultrafilters and maximal linked systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 365-388

Voir la notice de l'article provenant de la source Math-Net.Ru

The family of maximal linked systems all elements of which are sets of an arbitrary lattice with “zero” and “unit” is considered; its subfamily composed of ultrafilters of that lattice is also considered. Relations between natural topologies used to equip the set of maximal linked systems and the set of the lattice ultrafilters are investigated. It is demonstrated that the last set under natural (for ultrafilter spaces) equipment is a subspace of the space of maximal linked systems under equipment with two comparable topologies one of which is similar to the topology used for the Wallman extension and the second corresponds (conceptually) to the scheme of Stone space in the case when the initial lattice is an algebra of sets. Properties of the resulting bitopological structure are detailed for the cases when our lattice is an algebra of sets, a topology, and a family of closed sets in a topological space.
Keywords: lattice of sets, topology, ultrafilter. 
@article{VUU_2017_27_3_a6,
     author = {A. G. Chentsov},
     title = {Ultrafilters and maximal linked systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {365--388},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a6/}
}
TY  - JOUR
AU  - A. G. Chentsov
TI  - Ultrafilters and maximal linked systems
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2017
SP  - 365
EP  - 388
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a6/
LA  - ru
ID  - VUU_2017_27_3_a6
ER  - 
%0 Journal Article
%A A. G. Chentsov
%T Ultrafilters and maximal linked systems
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2017
%P 365-388
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a6/
%G ru
%F VUU_2017_27_3_a6
A. G. Chentsov. Ultrafilters and maximal linked systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 365-388. http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a6/