Geodesic
“Topologically Indexed Function Spaces and Adjoint Functors”
Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 169-178

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

Let Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-point space, we describe a class of right adjoints Top → Top/T, and then show that every right adjoint Top → Top/T is isomorphic to one of this form. We conclude by giving necessary and sufficient conditions for a left adjoint Top/T → Top to be isomorphic to one of the form − XTY, where Y is a space over T, and xT denotes the fiber product with the product topology. 
Niefield, S. B. “Topologically Indexed Function Spaces and Adjoint Functors”. Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 169-178. doi: 10.4153/CMB-1982-023-1
@article{10_4153_CMB_1982_023_1,
     author = {Niefield, S. B.},
     title = {{\textquotedblleft}Topologically {Indexed} {Function} {Spaces} and {Adjoint} {Functors{\textquotedblright}}},
     journal = {Canadian mathematical bulletin},
     pages = {169--178},
     year = {1982},
     volume = {25},
     number = {2},
     doi = {10.4153/CMB-1982-023-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-023-1/}
}
TY  - JOUR
AU  - Niefield, S. B.
TI  - “Topologically Indexed Function Spaces and Adjoint Functors”
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 169
EP  - 178
VL  - 25
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-023-1/
DO  - 10.4153/CMB-1982-023-1
ID  - 10_4153_CMB_1982_023_1
ER  - 
%0 Journal Article
%A Niefield, S. B.
%T “Topologically Indexed Function Spaces and Adjoint Functors”
%J Canadian mathematical bulletin
%D 1982
%P 169-178
%V 25
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-023-1/
%R 10.4153/CMB-1982-023-1
%F 10_4153_CMB_1982_023_1

[1] 1. Brown, R., Ten topologies on X × Y, Quart. J. Math, Oxford Series, (2) 14 (1963), 303-319. Google Scholar

[2] 2. R., Function spaces and product topologies, Quart J. Math, Oxford Series (2) 15 (1964), 228-250. Google Scholar

[3] 3. Day, B. J. and Kelly, G. M., On topological quotient maps preserved by pullbacks or products, Proc. Cambridge Plulos Soc 67 (1970) 553-558. Google Scholar

[4] 4. Fox, R. H., On topologies for function spaces Bull. Amer. Math Soc. 51 (1945), 429-432. Google Scholar

[5] 5. Hoffman, K.H. and Lawson, J. D., The spectral theory of distributive continuous lattices, Trans. Amer. Math. Soc 246 (1978), 285-310. Google Scholar

[6] 6. Isbell, J. R., Function spaces and adjoints, Math Scand 36, (1975) 317-339. Google Scholar

[7] 7. Isbell, J. R. Meet-continuous lattices, Sympos. Math 16, (1975) 41-54. Google Scholar

[8] 8. Kelley, J. L., General Topology, Graduate Texts in Mathematics no. 5, Springer-Verlag, 1971. Google Scholar

[9] 9. Niefield, S. B., Cartesianness : topological spaces, uniform spaces and affine schemes, accepted by Pure, J. and Applied Alg. Google Scholar

[10] 10. Scott, D. S., Continuous lattices, Springer Lecture Notes in Math 274 (1972), 97-136. Google Scholar

[11] 11. Spanier, E., Quasi-topologies, Duke Math J., 30 (1963), 1-14. Google Scholar

[12] 12. Steenrod, N. E., A convenient category of topological spaces, Michigan Math J. 14 (1967), 133-152. Google Scholar

[13] 13. Wilker, P. Adjoint product and horn functors in general topology, Pacific J. Math 34 (1970), 269-283. Google Scholar

Cité par Sources :