Geodesic
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

DOI

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.
DOI : 10.4153/CMB-1982-070-1
Mots-clés : 54F45 
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/}
}
TY  - JOUR
AU  - Rodé, Gerd
TI  - A Characterization of the Topological Dimension
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 487
EP  - 490
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-070-1/
DO  - 10.4153/CMB-1982-070-1
ID  - 10_4153_CMB_1982_070_1
ER  - 
%0 Journal Article
%A Rodé, Gerd
%T A Characterization of the Topological Dimension
%J Canadian mathematical bulletin
%D 1982
%P 487-490
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-070-1/
%R 10.4153/CMB-1982-070-1
%F 10_4153_CMB_1982_070_1

Cité par Sources :