Seminormal functors and paranormality
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 67-71 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is known that if a space $\mathcal{F}(X)$ is hereditarily paranormal for a paracompact $p$-space $X$ and normal functor $\mathcal{F}$ of degree $\ge 3$ in the category $\mathcal{P}$ of paracompact $p$-spaces and their perfect maps, then $X$ is metrizable. In this paper, a generalization of this theorem is proved for seminormal functors in the category $\mathcal{P}$.
@article{VMUMM_2023_2_a8,
     author = {A. A. Ivanov},
     title = {Seminormal functors and paranormality},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {67--71},
     year = {2023},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a8/}
}
TY  - JOUR
AU  - A. A. Ivanov
TI  - Seminormal functors and paranormality
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 67
EP  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a8/
LA  - ru
ID  - VMUMM_2023_2_a8
ER  - 
%0 Journal Article
%A A. A. Ivanov
%T Seminormal functors and paranormality
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 67-71
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a8/
%G ru
%F VMUMM_2023_2_a8
A. A. Ivanov. Seminormal functors and paranormality. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 67-71. http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a8/

[1] Engelking R., Obschaya topologiya, Mir, M., 1986

[2] Schepin E.V., “Funktory i neschetnye stepeni kompaktov”, Uspekhi matem. nauk, 36:3 (1981), 3–62 | MR | Zbl

[3] Fedorchuk V.V., “K teoreme Katetova o kube”, Vestn. Mosk. un-ta. Matem. Mekhan., 1989, no. 4, 93–96 | Zbl

[4] Dobrynina M. A., “K teoreme Fedorchuka o normalnom funktore”, Matem. zametki, 90:4 (2011), 630–633 | DOI | Zbl

[5] Kombarov A.P., “Ob odnoi slaboi forme normalnosti”, Vestn. Mosk. un-ta. Matem. Mekhan., 2017, no. 5, 48–51 | MR | Zbl

[6] Nyikos P., “Problem section: Problem B”, Topol. Proc., 9 (1984), 367 | Zbl

[7] Ivanov A.A., “Normalnye funktory i paranormalnost”, Vestn. Mosk. un-ta. Matem. Mekhan., 2021, no. 6, 51–53 | Zbl

[8] Ivanov A.V., “Teorema Katetova o kube i polunormalnye funktory”, Uch. zap. Petrozavod. gos. un-ta, 2012, no. 2, 104–108 | Zbl

[9] Arkhangelskii A.V., “Ob odnom klasse prostranstv, soderzhaschem vse metricheskie i vse lokalno bikompaktnye prostranstva”, Matem. sb., 67(109):1 (1965), 55–88 | Zbl

[10] Kombarov A.P., “Paranormalnost v topologicheskikh proizvedeniyakh”, Matem. zametki, 102:3 (2017), 477–480 | DOI | MR | Zbl