A Characterization of the Topological Dimension
Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 487-490
Voir la notice de l'article provenant de la source Cambridge University Press
This paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N 1,..., N K ), where N 1,..., N K , K are natural numbers. It is shown that a space X contains a system of faces of type (N 1,..., N K ) if and only if dim(X) ≥ N 1 + ... + N K . The two limit cases of the theorem, namely N k = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.
Rodé, Gerd. A Characterization of the Topological Dimension. Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 487-490. doi: 10.4153/CMB-1982-070-1
@article{10_4153_CMB_1982_070_1,
author = {Rod\'e, Gerd},
title = {A {Characterization} of the {Topological} {Dimension}},
journal = {Canadian mathematical bulletin},
pages = {487--490},
year = {1982},
volume = {25},
number = {4},
doi = {10.4153/CMB-1982-070-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-070-1/}
}
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