Geodesic
On transformations of families of pseudometrics
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 19-32.

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

Arbitrary transformations of a family of pseudometrics are studied which result in uniform continuous pseudometrics again. Then their properties are applied for a description of a quotient uniform structure by means of pseudometrics on the initial space. It is proved that if a uniform structure on this space is subinvariant with respect to some given set of its transformations then the quotient uniform structure is subinvariant with respect to the induced transformations. The minimization for a given family of pseudometrics is considered in the last section. 
@article{FPM_2001_7_1_a1,
     author = {B. G. Averbukh},
     title = {On transformations of families of pseudometrics},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {19--32},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a1/}
}
TY  - JOUR
AU  - B. G. Averbukh
TI  - On transformations of families of pseudometrics
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2001
SP  - 19
EP  - 32
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a1/
LA  - ru
ID  - FPM_2001_7_1_a1
ER  - 
%0 Journal Article
%A B. G. Averbukh
%T On transformations of families of pseudometrics
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 19-32
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a1/
%G ru
%F FPM_2001_7_1_a1
B. G. Averbukh. On transformations of families of pseudometrics. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 19-32. http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a1/