Geodesic
Relatively coarse sequential convergence
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 395-408.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense group precompletion of the group of rational numbers (equipped with the usual metric convergence) is complete; (ii) there are exactly $\exp \exp \omega $ such completions; (iii) the real line is the only one of them the convergence of which is Fréchet. Analogous results hold for the relatively coarse dense field precompletions of the subfield of all complex numbers both coordinates of which are rational numbers.
Classification : 16W99, 20K35, 20K45, 54A20, 54H11, 54H13
Keywords: Sequential convergence: compatible-; coarse-; relatively coarse-; FLUSH-group; FLUSH-ring; completion; extension 
@article{CMJ_1997__47_3_a1,
     author = {Fri\v{c}, Roman and Zanolin, Fabio},
     title = {Relatively coarse sequential convergence},
     journal = {Czechoslovak Mathematical Journal},
     pages = {395--408},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {1997},
     mrnumber = {1461420},
     zbl = {0897.54002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a1/}
}
TY  - JOUR
AU  - Frič, Roman
AU  - Zanolin, Fabio
TI  - Relatively coarse sequential convergence
JO  - Czechoslovak Mathematical Journal
PY  - 1997
SP  - 395
EP  - 408
VL  - 47
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a1/
LA  - en
ID  - CMJ_1997__47_3_a1
ER  - 
%0 Journal Article
%A Frič, Roman
%A Zanolin, Fabio
%T Relatively coarse sequential convergence
%J Czechoslovak Mathematical Journal
%D 1997
%P 395-408
%V 47
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a1/
%G en
%F CMJ_1997__47_3_a1
Frič, Roman; Zanolin, Fabio. Relatively coarse sequential convergence. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 395-408. http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a1/