Geodesic
Elementarity and Dimensions
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 292-298 
K. P. Hart. Elementarity and Dimensions. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 292-298. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a14/
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     title = {Elementarity and {Dimensions}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An alternative proof of Fedorchuk's recent result that $\dim X\le\operatorname{Dg}X$ for compact Hausdorff spaces X is given. The problem is reduced to the metric case by using the Lowenheim–Skolem theorem.

[1] Engelking R., General Topology. Revised and completed edition, Sigma Series in Pure Mathematics, no. 6, Heldermann Verlag, Berlin, 1989 | MR | Zbl

[2] Brouwer L. E. J., “Über den natürlichen Dimensionsbegriff”, Journal für die reine und angewandte Mathematik, 142 (1913), 146–152

[3] Fedorchuk V. V., Levin M., Schepin E. V., “O brauerovskom opredelenii razmernosti”, UMN, 54:2 (326) (1999), 193–194 | MR | Zbl

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

[5] Wallman H., “Lattices and topological spaces”, Ann. of Math., 39 (1938), 112–126 | DOI | MR | Zbl

[6] Hart K. P., van Mill J., Pol R., “Remarks on hereditarily indecomposable continua”, Proceedings of the 15th Summer Conference on General Topology and its Applications/1st Turkish International Conference on Topology and its Applications (Oxford, OH/Istanbul, 2000), 25, 2002, 179–206 | MR

[7] van der Steeg B., Models in Topology, Ph. D. thesis, TU Delft, 2003

[8] Hodges W., A Shorter Model Theory, Cambridge Univ. Press, Cambridge, 1997 | MR

[9] Hemmingsen E., “Some theorems in dimension theory for normal Hausdorff spaces”, Duke Math. J., 13 (1946), 495–504 | DOI | Zbl

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