Properties of covers in the lattice of group topologies for nilpotent groups

V. I. Arnautov

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2012), pp. 38-44.

Résumé

A nilpotent group $\hat{G}$ and two group topologies ${\hat{\tau }}^{″}$ and $\hat{\tau }\ast$ on $\hat{G}$ are constructed such that $\hat{\tau }\ast$ is a coatom in the lattice of all group topologies of the group $\hat{G}$ and such that between $inf\{{\hat{\tau }}^{″},{\hat{\tau }}_d\}$ and $inf\{{\hat{\tau }}^{″},\hat{\tau }\ast \}$ there exists an infinite chain of group topologies.

Bibliographie

[1] Arnautov V. I., Topala A. Gh., “An example of ring with non-modular lattice of ring topologies”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 1998, no. 2(27), 130–131 | MR | Zbl

[2] Arnautov V. I., “Properties of finite unrefinable chais of groups topologies”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2009, no. 2(60), 1–17 | MR

[3] Bourbaki N., Obshchaya topologiya. Osnovnye structury (General Topology, Fundamental Structures), Moscow, 1958, 324 pp. (in Russian)