Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
Ky Fan · Proceedings of the National Academy of Sciences · 1952
3See §9, 10 in a forthcoming paper on Track Groups by M. G. Barratt, concerning the homotopy groups of function spaces Xp.The group in question is vs-[(.S%-)y2 "xe where xo is an inessential map.4 Whitehead, J. H. C., "A Note on Suspension," Q.J. Math.(Oxford) (2), 1, 9-22 (1950).See also reference 2.'See reference 3, §2.A map q:P P Q induces a homomorphism 9i*:rk(XAQ)-Tk(Xp) for a large class of spaces P, Q, X.6 Hilton, P. J., "The Calculation of Homotopy Groups of A.2-polyhedra (II)," Ibid.,(2), 2,228-240(1951).Theorem 1.3 settles the problems stated on pages 234 and 240.7Eckmann, B., "Zur Homotopietheorie Gefaserter Raume," Comm.Math.Helvetici, 14, 141-192 (1941); also "Uber Homotopiegruppen fon Gruppenraumen," Ibid., 14, 234-256(1941).