Geodesic
On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 53-57

Voir la notice de l'article provenant de la source Cambridge University Press

Let (X, τ) be a Tychonov space and the collection of all families of pseudometrics on X generating the topology τ on X. Let f:X→X and c>0. Then f is said to be a topological c-homothety if there exists some B in such that d(f(x), f(y))=cd(x, y) for all d ∈ B and all x, y in X (see [4]). We say that f can be linearized in L as a c-homothety if there exists a linear topological space L, and a topological embedding i:X→L such that i(f(x))=c i(x) for all x in X (see [4]).f is said to be squeezing if for some a in X.
DOI : 10.4153/CMB-1976-006-2
Mots-clés : 54.35, 54.6, 54.85, Topological c-homothety, Linear representations of selfmaps 
Chew, Kim-Peu; Tan, Kok-Keong. On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 53-57. doi: 10.4153/CMB-1976-006-2
@article{10_4153_CMB_1976_006_2,
     author = {Chew, Kim-Peu and Tan, Kok-Keong},
     title = {On the {Representation} of {Mappings} of {Tychonov} {Spaces} as {Restrictions} of {Linear} {Transformations}},
     journal = {Canadian mathematical bulletin},
     pages = {53--57},
     year = {1976},
     volume = {19},
     number = {1},
     doi = {10.4153/CMB-1976-006-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-006-2/}
}
TY  - JOUR
AU  - Chew, Kim-Peu
AU  - Tan, Kok-Keong
TI  - On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations
JO  - Canadian mathematical bulletin
PY  - 1976
SP  - 53
EP  - 57
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-006-2/
DO  - 10.4153/CMB-1976-006-2
ID  - 10_4153_CMB_1976_006_2
ER  - 
%0 Journal Article
%A Chew, Kim-Peu
%A Tan, Kok-Keong
%T On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations
%J Canadian mathematical bulletin
%D 1976
%P 53-57
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-006-2/
%R 10.4153/CMB-1976-006-2
%F 10_4153_CMB_1976_006_2

[1] 1. Edelstein, M., On the representation of mappings of compact metrizable spaces as restrictions of linear transformations, Can. J. Math. Vol. XXII (1970) 372–375. Google Scholar

[2] 2. Edelstein, M. and Swaminathan, S., On the representation of mappings of normal Hausdorff spaces as restrictions of linear transformations, Roma Accademia Nazionale Del Lindel. Serie VIII, Vol. L (1971) 676–678. Google Scholar

[3] 3. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, Princeton, N.J. (1960). Google Scholar

[4] 4. Janos, L., Topological homothetics on compact Hausdorff spaces, Proc. Amer. Math. Soc. Vol. 21 (1969) 562–568. Google Scholar

Cité par Sources :