Geodesic
An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different
Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1809-1822 
V. V. Fedorchuk. An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different. Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1809-1822. http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/
@article{SM_2004_195_12_a6,
     author = {V. V. Fedorchuk},
     title = {An example of a~compact {Hausdorff} space whose {Lebesgue,} {Brouwer,} and inductive dimensions are different},
     journal = {Sbornik. Mathematics},
     pages = {1809--1822},
     year = {2004},
     volume = {195},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/}
}
TY  - JOUR
AU  - V. V. Fedorchuk
TI  - An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different
JO  - Sbornik. Mathematics
PY  - 2004
SP  - 1809
EP  - 1822
VL  - 195
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/
LA  - en
ID  - SM_2004_195_12_a6
ER  - 
%0 Journal Article
%A V. V. Fedorchuk
%T An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different
%J Sbornik. Mathematics
%D 2004
%P 1809-1822
%V 195
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/
%G en
%F SM_2004_195_12_a6

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

We construct an example of a separable compact Hausdorff space $B$ satisfying the first countability axiom of dimension $2=\dim B<\operatorname{Dg}B=3<\operatorname{ind}B=4=\operatorname{Ind}B$, where $\operatorname{Dg}$ is the inductive dimension invariant introduced by Brouwer in 1913 under the name “Dimensionsgrad”.

[1] Brouwer L. E. J., “Über den natulichen Dimensionbegriff”, J. Reine Angew. Math., 142 (1913), 145–152

[2] Gurevich V., Volmen G., Teoriya razmernosti, IL, M., 1948

[3] Fedorchuk V. V., Levin M., Schepin E. V., “O brauerovskom opredelenii razmernosti”, UMN, 54:2 (1999), 193–194 | MR | Zbl

[4] Fedorchuk V. V., van Mill J., “Dimensionsgrad for locally connected Polish spaces”, Fund. Math., 163:1 (2000), 77–82 | MR | Zbl

[5] Fedorchuk V. V., “O brauerovskoi razmernosti bikompaktov”, Matem. zametki, 73:2 (2003), 295–304 | MR | Zbl

[6] Aleksandrov P. S., Pasynkov B. A., Vvedenie v teoriyu razmernosti, Nauka, M., 1973 | MR

[7] Engelking R., Sieklucki K., Topology. A geometric approach, Heldermann, Berlin, 1992 | MR | Zbl

[8] van Mill J., The infinite-dimensional topology of function spaces, Elsevier, Amsterdam, 2001

[9] Mazurkiewicz S., “O arytmetizacji continuow”, C. R. Varsovie, 10 (1913), 171–177

[10] Fedorchuk V. V., “Ob otobrazheniyakh, ne ponizhayuschikh razmernost”, Dokl. AN SSSR, 185:1 (1968), 54–57

[11] Fedorchuk V. V., “O silno zamknutykh otobrazheniyakh”, Dokl. AN SSSR, 187:1 (1969), 47–49 | MR | Zbl

[12] Savinov N. V., “O vpolne zamknutykh otobrazheniyakh”, Vestn. MGU. Ser. 1. Matem., mekh., 1975, no. 3, 39–45 | MR | Zbl

[13] Fedorchuk V. V., “O bikompaktakh s nesovpadayuschimi razmernostyami”, Dokl. AN SSSR, 182:2 (1968), 275–277 | MR | Zbl

[14] Fedorchuk V. V., “Bikompakty bez promezhutochnykh razmernostei”, Dokl. AN SSSR, 213:4 (1973), 795–797 | MR | Zbl

[15] Fedorchuk V. V., “Primer odnorodnogo bikompakta s nesovpadayuschimi razmernostyami”, Dokl. AN SSSR, 198:6 (1971), 1283–1286 | MR | Zbl

[16] Chatyrko V. A., “O zmeevidnykh bikompaktakh”, Vestn. MGU. Ser. 1. Matem., mekh., 1984, no. 4, 15–19 | MR | Zbl