Geodesic
Some categorical properties of the functors $O_\tau$ and $O_R$ of weakly additive functionals
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 681-693 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, the spaces of weakly additive $\tau$-smooth and Radon functionals are investigated. It is proved that the functors of weakly additive $\tau$-smooth and Radon functionals weakly preserve the density of Tychonoff spaces, and the functor of weakly additive $\tau$-smooth functionals forms a monad in the category of Tychonoff spaces and their continuous mappings. Examples and remarks are given showing that these functors fail to satisfy certain Shchepin normality conditions. Problems having positive solutions for normal functors are presented. 
@article{MZM_2006_79_5_a4,
     author = {A. A. Zaitov},
     title = {Some categorical properties of the functors $O_\tau$ and $O_R$ of weakly additive functionals},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--693},
     year = {2006},
     volume = {79},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a4/}
}
TY  - JOUR
AU  - A. A. Zaitov
TI  - Some categorical properties of the functors $O_\tau$ and $O_R$ of weakly additive functionals
JO  - Matematičeskie zametki
PY  - 2006
SP  - 681
EP  - 693
VL  - 79
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a4/
LA  - ru
ID  - MZM_2006_79_5_a4
ER  - 
%0 Journal Article
%A A. A. Zaitov
%T Some categorical properties of the functors $O_\tau$ and $O_R$ of weakly additive functionals
%J Matematičeskie zametki
%D 2006
%P 681-693
%V 79
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a4/
%G ru
%F MZM_2006_79_5_a4
A. A. Zaitov. Some categorical properties of the functors $O_\tau$ and $O_R$ of weakly additive functionals. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 681-693. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a4/

[1] Banakh T. O., “Topologiya prostranstv veroyatnostnykh mer. I: Funktory $P_\tau$ i $\widehat P$”, Matematichni studii, 5 (1995), 65–87 | MR | Zbl

[2] Zaitov A. A., “$\tau$-gladkie slabo additivnye funktsionaly i veroyatnostnye mery”, Tezisy dokl. konf. molodykh uchenykh, posvyaschennoi 60-letiyu AN RUz, 2003, 41–42

[3] Schepin E. V., “Funktory i neschetnye stepeni kompaktov”, UMN, 36:3(219) (1981), 3–62 | Zbl

[4] Radul T. N., “On the functor of order-preserving functionals”, Comment. Math. Univ. Carol., 39:3 (1998), 609–615 | MR | Zbl

[5] Chigogidze A. Ch., “O prodolzhenii normalnykh funktorov”, Vestn. MGU. Ser. matem., mekh., 1984, no. 6, 23–26 | Zbl

[6] Fedorchuk V. V., “Veroyatnostnye mery v topologii”, UMN, 46:1 (1991), 41–80 | Zbl

[7] Beshimov R. B., “On weakly additive functionals”, Matematychni Studii, 18:2, 179–186 | MR | Zbl

[8] Zaitov A. A., “On categorical properties of the functor of order-preserving functionals”, Methods of Functional Analysis and Topology, 9:4 (2003), 357–364 | MR | Zbl

[9] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, Izd-vo MGU, M., 1988 | Zbl

[10] Fedorchuk V. V., Sadovnichii Yu. V., “O nekotorykh topologicheskikh i kategornykh svoistvakh znakoperemennykh mer”, Fundament. i prikladnaya matem., 5:2 (1999), 597–618 | MR | Zbl

[11] Fedorchuk V. V., “Mnogoznachnye retraktsii i kharakterizatsiya $n$-myagkikh otobrazhenii”, Tr. MMO, 51, URSS, M., 1988, 169–207 | Zbl

[12] Eilenberg S., Moore J., “Adjoint functors and triples”, Ill. J. Math., 9:3 (1965), 381–398 | MR | Zbl