Right adjoint for the smash product functor

Cagliari, Francesca

doi:10.1090/S0002-9939-96-03065-1

Right adjoint for the smash product functor
HTML articles powered by AMS MathViewer

by Francesca Cagliari PDF

Proc. Amer. Math. Soc. 124 (1996), 1265-1269 Request permission

Abstract:

The smash-product functor $(\text {–})\wedge x_0$ in the category $\underline {\mathbf {Top}}_*$ of pointed topological spaces has a right adjoint for any choice of the base point $x_0$, if and only if the topological space $X$ is quasi-locally compact, that is, if and only if the product functor $(\text {–})\times X$ has a right adjoint in the category $\underline {\mathbf {Top}}$ of topological spaces.

References

A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
C. H. Cook and H. R. Fisher, On equicontinuity and continuous convergenge, Math. Ann. 159 (1965), 94–104.
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
B. J. Day and G. M. Kelly, On topological quotient maps preserved by pullbacks or products, Proc. Cambridge Philos. Soc. 67 (1970), 553–558. MR 254817, DOI 10.1017/s0305004100045850
Albert Eagle, Series for all the roots of the equation $(z-a)^m=k(z-b)^n$, Amer. Math. Monthly 46 (1939), 425–428. MR 6, DOI 10.2307/2303037
Dale Husemoller, Fibre bundles, McGraw-Hill Book Co., New York-London-Sydney, 1966. MR 0229247
Karl H. Hofmann and Jimmie D. Lawson, The spectral theory of distributive continuous lattices, Trans. Amer. Math. Soc. 246 (1978), 285–310. MR 515540, DOI 10.1090/S0002-9947-1978-0515540-7
I. M. James, General topology and homotopy theory, Springer-Verlag, New York, 1984. MR 762634, DOI 10.1007/978-1-4613-8283-6
John R. Isbell, Function spaces and adjoints, Math. Scand. 36 (1975), no. 2, 317–339. MR 405340, DOI 10.7146/math.scand.a-11581
Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
Charles Richard Francis Maunder, Algebraic topology, Cambridge University Press, Cambridge-New York, 1980. MR 694843
Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581