caa a22 4500 475741315 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/BF02675799 doi (NATIONALLICENCE)springer-10.1007/BF02675799 Frenkin B. Central Institute of Mathematical Economics, Russian Academy of Sciences, Moscow aut Some topological minimax theorems [Elektronische Daten] [B. Frenkin] Two topological variants of the minimax theorem are proved with no restrictions on one of the spaces except for those related to the function under consideration. The conditions concerning the behavior of the function deal only with the interval between the maximin and minimax. As corollaries, we obtain the well-known theorems of Sion and Hoang-Tui on quasiconvex-quasiconcave semicontinuous functions. The scheme of arguments goes back to the Hahn-Banach theorem and the separating hyperplane theorem. It is shown how this scheme can be explicitly realized in the proof of the Hahn-Banach theorem. Kluwer Academic/Plenum Publishers, 2000 minimax and maximin nationallicence quasiconvex and quasiconcave functions nationallicence semicontinuous functions nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 112-118 0001-4346 67:1<112 2000 67 11006 https://doi.org/10.1007/BF02675799 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675799 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Frenkin B. Central Institute of Mathematical Economics, Russian Academy of Sciences, Moscow aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 112-118 0001-4346 67:1<112 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer