Geodesic
On one-to-one mappings of countably compact spaces onto Hausdorff compact spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 871-880 
A. V. Arkhangel'skii; V. V. Fedorchuk. On one-to-one mappings of countably compact spaces onto Hausdorff compact spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 871-880. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a2/
@article{FPM_1995_1_4_a2,
     author = {A. V. Arkhangel'skii and V. V. Fedorchuk},
     title = {On one-to-one mappings of countably compact spaces onto {Hausdorff} compact spaces},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {871--880},
     year = {1995},
     volume = {1},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a2/}
}
TY  - JOUR
AU  - A. V. Arkhangel'skii
AU  - V. V. Fedorchuk
TI  - On one-to-one mappings of countably compact spaces onto Hausdorff compact spaces
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1995
SP  - 871
EP  - 880
VL  - 1
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a2/
LA  - ru
ID  - FPM_1995_1_4_a2
ER  - 
%0 Journal Article
%A A. V. Arkhangel'skii
%A V. V. Fedorchuk
%T On one-to-one mappings of countably compact spaces onto Hausdorff compact spaces
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1995
%P 871-880
%V 1
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a2/
%G ru
%F FPM_1995_1_4_a2

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

We deal with the following problem: is it correct that every separable, countably compact, first countable space admits a one-to-one mapping onto some Hausdorff compact space? Theorems 2 and 3 show that this problem has no positive solution in ZFC.

[1] Fedorchuk V. V., “Vpolne zamknutye otobrazheniya i sovmestimost nekotorykh teorem obschei topologii s aksiomami teorii mnozhestv”, Matem. sb., 99:1 (1976), 3–33 | MR | Zbl

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

[3] Fedorchuk V. V., “Sovmestimost nekotorykh teorem obschei topologii s aksiomami teorii mnozhestv”, Dokl. AN SSSR, 222:2 (1975), 302–305 | MR | Zbl

[4] Ostaszewski A., “On countably compact, perfectly normal spaces”, J. London Math. Soc., 14 (1976), 505–516 | DOI | MR | Zbl

[5] Franklin S. P., Rajagopalan M., “Some examples in topology”, Trans. Amer. Math. Soc., 155 (1971), 305–314 | DOI | MR | Zbl

[6] Hajnal A., Juhasz I., “A separable normal topological group need not be Lindelöf”, General Topology and Appl., 6:2 (1976), 199–205 | DOI | MR | Zbl

[7] Comfort W. W., Ross K. A., “Pseudocompactness and uniform continuity in topological groups”, Pacific J. Math., 16 (1966), 483–496 | MR | Zbl

[8] Comfort W. W., “Topological groups”, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1143–1264 | MR

[9] Arhangel'skii A. V., “On countably compact topologies on compact groups and on dyadic compacta”, Topology and Appl., 57 (1994), 163–181 | DOI | MR

[10] Hagler J., “On the structure of $S$ and $C(S)$ for $S$ dyadic”, Trans. Amer. Math. Soc., 214 (1975), 415–428 | DOI | MR | Zbl

[11] Gerlits J., “On subspaces of dyadic compacta”, Studia Sci. Math. Hungar., 11 (1976), 115–120 | MR | Zbl

[12] Efimov B. A., “Otobrazheniya i vlozheniya diadicheskikh prostranstv”, Matem. sb., 103:1 (1977), 52–68 | MR | Zbl

[13] Nyikos P., “On first countable, countably compact spaces III: The problem of obtaining separable noncompact examples”, Open Problems in Topology, North Holland, Amsterdam, 1990, 127–161 | MR