Communications of the
Korean Mathematical Society CKMS

In a paper by Hou Jicheng, $On$ $some$ $KKM$ $type$ $theorems$, Advaces in Mathematics $\bf 36$ (2007), no. 1, 86--88, the author claimed that some previous KKM type theorems are false by giving a counterexample. In the present paper, we show that the counterexample does not work and, consequently, the results are correct. Moreover, we claim that the artificial concept like transfer compactly closed-valued maps can be destroyed. Finally, we introduce a theorem generalizing the main target of Hou.

Keywords: KKM type theorems, admissible class of multimaps, transfer compactly closedness

MSC numbers: 47H04, 47H10, 49J27, 49J35, 54C60, 54H25, 91B50