Normality-type properties and covariant functors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 2, pp. 57-98 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Topological properties similar to normality are considered in subspaces of products and powers of topological spaces, of spaces of closed subsets, and of spaces having the form $\mathcal{F}(X)$, where $\mathcal{F}$ is a normal functor.
@article{FPM_2003_9_2_a1,
     author = {A. P. Kombarov},
     title = {Normality-type properties and covariant functors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {57--98},
     year = {2003},
     volume = {9},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_2_a1/}
}
TY  - JOUR
AU  - A. P. Kombarov
TI  - Normality-type properties and covariant functors
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2003
SP  - 57
EP  - 98
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2003_9_2_a1/
LA  - ru
ID  - FPM_2003_9_2_a1
ER  - 
%0 Journal Article
%A A. P. Kombarov
%T Normality-type properties and covariant functors
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2003
%P 57-98
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2003_9_2_a1/
%G ru
%F FPM_2003_9_2_a1
A. P. Kombarov. Normality-type properties and covariant functors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 2, pp. 57-98. http://geodesic.mathdoc.fr/item/FPM_2003_9_2_a1/

[1] Aleksandrov P. S., Uryson P. S., Memuar o kompaktnykh topologicheskikh prostranstvakh, Nauka, M., 1971 | MR

[2] Arkhangelskii A. V., “Ob odnom klasse prostranstv, soderzhaschem vse metricheskie i vse lokalno bikompaktnye prostranstva”, Mat. sb., 67 (1965), 55–85

[3] Arkhangelskii A. V., Ponomarev V. I., Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974 | MR

[4] Basmanov V. N., “O funktorakh, perevodyaschikh svyaznye $ANR$-bikompakty v odnosvyaznye prostranstva”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1984, no. 6, 40–42 | MR | Zbl

[5] Velichko N. V., “O prostranstve zamknutykh podmnozhestv”, Sib. mat. zhurn., 16 (1975), 627–629 | Zbl

[6] Gulko S. P., “O svoistvakh mnozhestv, lezhaschikh v $\Sigma$-proizvedeniyakh”, DAN SSSR, 237 (1977), 505–508 | MR

[7] Zhuraev T. F., “Normalnye funktory i metrizuemost bikompaktov”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 2000, no. 4, 8–11 | MR | Zbl

[8] Ivanova V. M., “K teorii prostranstv podmnozhestv”, DAN SSSR, 101 (1955), 601–603 | MR | Zbl

[9] Kombarov A. P., “O tesnote i normalnosti $\Sigma$-proizvedenii”, DAN SSSR, 239 (1978), 775–778 | MR | Zbl

[10] Kombarov A. P., “Tesnota parakompaktnykh $k$-prostranstv i schetnaya parakompaktnost $F_{\sigma}$-mnozhestv v proizvedeniyakh”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1990, no. 3, 87–89 | MR | Zbl

[11] Kombarov A. P., “Psevdonormalnost $F_\sigma$-podmnozhestv $X^2\setminus\Delta$”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1991, no. 1, 85–87 | MR

[12] Kombarov A. P., Malykhin V. I., “O $\Sigma$-proizvedeniyakh”, DAN SSSR, 213 (1973), 774–776 | MR | Zbl

[13] Malykhin V. I., “O tesnote i chisle Suslina v $\exp X$ i v proizvedenii prostranstv”, DAN SSSR, 203 (1972), 1001–1003 | Zbl

[14] Malykhin V. I., Shapirovskii B. E., “Aksioma Martina i svoistva topologicheskikh prostranstv”, DAN SSSR, 213 (1973), 532–535 | Zbl

[15] Malykhin D. V., “Schetno kompaktnoe $\nabla$-normalnoe prostranstvo imeet schetnyi kharakter”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1997, no. 5, 31–33 | MR | Zbl

[16] Pontryagin L. S., Nepreryvnye gruppy, M.–L., 1938

[17] Popov V. V., “O prostranstve zamknutykh podmnozhestv”, DAN SSSR, 229:5 (1976), 1051–1054 | MR | Zbl

[18] Fedorchuk V. V., “K teoreme Katetova o kube”, Vestnik Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1989, no. 4, 93–96 | MR | Zbl

[19] Fedorchuk V. V., Filippov V. V., Obschaya topologiya, Izd-vo Mosk. un-ta, M., 1988 | Zbl

[20] Choban M. M., Mnogoznachnye otobrazheniya i ikh prilozheniya, Diss. $\dots$ dokt. fiz.-mat. nauk, Tbilisi, 1979

[21] Shapirovskii B. E., “O prostranstvakh s usloviem Suslina i Shanina”, Mat. zametki, 15:2 (1974), 281–288

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

[23] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[24] Arhangel'skii A. V., Kombarov A. P., “On $\nabla$-normal spaces”, Topol. Appl., 35 (1990), 121–126 | DOI | MR

[25] Arhangel'skii A. V., “Divisibility and cleavability of spaces”, Recent developments of general topology and its applications (Berlin, 1992), Math. Res., 67, Akademie-Verlag,, Berlin, 1992, 13–26 | MR

[26] Brandenburg H., “Separating closed sets by continuous mappings into developable spaces”, Canad. J. Math., 33 (1981), 1420–1431 | DOI | MR | Zbl

[27] Chaber J., “Conditions which imply compactness in countably compact spaces”, Bull. Acad. Polon. Sci. Ser. Sci. Math., Astronom., Phys., 24 (1976), 993–998 | MR

[28] Chiba K., “The strong paracompactness of $\sigma$-products”, Sci. Math., 2 (1999), 285–292 | MR | Zbl

[29] Corson H. H., “Normality in subsets of product spaces”, Amer. J. Math., 81 (1959), 785–796 | DOI | MR | Zbl

[30] Daniel T., Gruenhage G., “Some nonnormal $\Sigma$-products”, Topol. Appl., 43 (1992), 19–25 | DOI | MR | Zbl

[31] Van Douwen E. K., “The Pixley–Roy topology on spaces of subsets”, Set-Theoretic Topology, ed. G. M. Reed, Academic Press, New York, 1977, 111–134 | MR

[32] Van Douwen E. K., “Covering and separation properties of box products”, Surveys in General Topology, ed. G. M. Reed, Academic Press, New York, 1980, 55–129 | MR

[33] Van Douwen E. K., “The integers and topology”, Handbook of Set-Theoretic Topology, eds. K. Kunen and J. E. Vaughan, North-Holland, Amsterdam, 1984, 111–167 | MR

[34] Eda K., Gruenhage G., Koszmider P., Tamano K., “Todorčević S.”, Topol. Appl., 67 (1995), 189–220 | DOI | MR | Zbl

[35] Engelking R., “On functions defined on Cartesian products”, Fund. Math., 59 (1966), 221–231 | MR | Zbl

[36] Glicksberg I., “Stone–Čech compactifications of products”, Trans. Amer. Math. Soc., 90 (1959), 369–382 | DOI | MR | Zbl

[37] Good C., Tree I. J., “On ${\delta}$-normality”, Topol. Appl., 56 (1994), 117–127 | DOI | MR | Zbl

[38] Gruenhage G., “Covering properties on $X^2\setminus\Delta$, $W$-sets, and compact subsets of $\Sigma$-products”, Topol. Appl., 17 (1984), 287–304 | DOI | MR | Zbl

[39] Gruenhage G., Nyikos P. J., “Normality in $X^2$ for compact $X$”, Trans. Amer. Math. Soc., 340 (1993), 563–586 | DOI | MR | Zbl

[40] K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984 | MR | Zbl

[41] Katětov M., “Complete normality of Cartesian products”, Fund. Math., 35 (1948), 271–274 | MR | Zbl

[42] Keesling J., “On the equivalence of normality and compactness in hyperspaces”, Pacific J. Math., 33 (1970), 657–667 | MR | Zbl

[43] Kister J. M., “Uniform continuity and compactness in topological groups”, Proc. Amer. Math. Soc., 13 (1962), 37–40 | DOI | MR | Zbl

[44] Kombarov A. P., “On expandable discrete collections”, Topol. Appl., 69 (1996), 283–292 | DOI | MR | Zbl

[45] Kombarov A. P., “On $F_{\sigma}$-${\delta}$-normality and hereditary ${\delta}$-normality”, Topol. Appl., 91 (1999), 221–226 | DOI | MR | Zbl

[46] Kombarov A. P., “Normal functors and generalized normality”, International Conference on Functional Analysis and its Applications (Dedicated to the 110th anniversary of Stefan Banach), Abstracts, Lviv, Ukraine, 2002, 109

[47] Larson P., Todorčević S., “Katětov's problem”, Trans. Amer. Math. Soc., 354 (2002), 1783–1791 | DOI | MR | Zbl

[48] Mack J., “Countable paracompactness and weak normality properties”, Trans. Amer. Math. Soc., 148 (1970), 265–272 | DOI | MR | Zbl

[49] Noble N., “Products with closed projections, II”, Trans. Amer. Math. Soc., 160 (1971), 169–183 | DOI | MR | Zbl

[50] Nogura T., “Tightness of compact Hausdorff spaces and normality of product spaces”, J. Math. Soc. Japan, 28 (1976), 360–362 | DOI | MR | Zbl

[51] Nyikos P., “A compact nonmetrizable space $P$ such that $P^2$ is completely normal”, Topol. Proc., 2 (1977), 359–363 | MR

[52] Pareek C. M., “Characterizations of $p$-spaces”, Canad. Math. Bull., 14 (1971), 459–460 | DOI | MR | Zbl

[53] Proctor C. W., “A separable pseudonormal nonmetrizable Moore space”, Bull. Acad. Polon. Sci. Ser. Sci. Math., Astronom., Phys., 18 (1970), 179–181 | MR | Zbl

[54] Stone A. H., “Paracompactness and product spaces”, Bull. Amer. Math. Soc., 54 (1948), 977–982 | DOI | MR | Zbl

[55] Vietoris L., “Bereiche zweiter Ordnung”, Monatsh. Math. Phys., 1922, no. 32, 258–280 | DOI | MR | Zbl

[56] Weiss W., “Countably compact spaces and Martin's axiom”, Canad. J. Math., 30 (1978), 243–249 | DOI | MR | Zbl

[57] Zenor P., “Countable paracompactness in product spaces”, Proc. Amer. Math. Soc., 30 (1971), 199–201 | DOI | MR | Zbl

[58] Zenor P., “Countable paracompactness of $F_{\sigma}$-sets”, Proc. Amer. Math. Soc., 55 (1976), 201–202 | DOI | MR | Zbl