In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology.
- Every metrisable locally convex space with continuous dual carries the Mackey topology, that is , or to put it more succinctly every Mackey space carries the Mackey topology
- Every Fréchet space carries the Mackey topology and the topology coincides with the strong topology, that is
The Mackey topology has an application in economies with infinitely many commodities.
- A.I. Shtern (2001), "Mackey topology", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Mackey, G.W. (1946). "On convex topological linear spaces". Trans. Amer. Math. Soc. Transactions of the American Mathematical Society, Vol. 60, No. 3. 60 (3): 519–537. JSTOR 1990352. doi:10.2307/1990352.
- Bourbaki, Nicolas (1977). Topological vector spaces. Elements of mathematics. Addison–Wesley.
- Robertson, A.P.; W.J. Robertson (1964). Topological vector spaces. Cambridge Tracts in Mathematics. 53. Cambridge University Press. p. 62.
- Schaefer, Helmuth H. (1971). Topological vector spaces. GTM. 3. New York: Springer-Verlag. p. 131. ISBN 0-387-98726-6.