COMMENTS ON DING'S EXAMPLES OF FC-SPACES AND RELATED MATTERS Park, Se-Hie;
Recently Ding [4, 5, 8] gives examples of his FC-spaces which are not L-spaces due to Ben-El-Mechaiekh et al. . We show that they are actually L-spaces. We also clarify that all statements in  can be stated in corrected and generalized forms for the class of abstract convex spaces beyond FC-spaces.
H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano, and J.-V. Llinares, Abstract convexity and fixed points, J. Math. Anal. Appl. 222 (1998), no. 1, 138-150.
F.-P. Deng and L. Wang, Coincidence theorems in product FC-spaces, J. Sichuan Normal Univ. (Nat. Sci) 32 (2009), no. 3, 297-300.
L. Deng and X.-Y. Zang, A parametric type of KKM theorem in FC-spaces with applications, Appl. Math. Mech. (English Ed.) 30 (2009), no. 1, 73-79.
X. P. Ding, Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications. I, Appl. Math. Mech. (English Ed.) 28 (2007), no. 12, 1561-1568.
X. P. Ding, Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces, Nonlinear Anal. 70 (2009), no. 2, 881-889.
X. P. Ding, Pareto equilibria for generalized constrained multiobjective games in FC-spaces without local convexity structure, Nonlinear Anal. 71 (2009), no. 11, 5229-5237.
X. P. Ding, Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces, Appl. Math. Mech. (English Ed.) 30 (2009), no. 3, 263-274.
X. P. Ding, New systems of generalized vector quasi-equilibrium problems in product FC-spaces, J. Global Optim. 46 (2010), no. 1, 133-146.
X. P. Ding, Collective fixed points, generalized games and systems of generalized quasivariational inclusion problems in topological spaces, Nonlinear Anal. 73 (2010), no. 6, 1834-1841.
X. P. Ding and H. R. Feng, Fixed point theorems and existence of equilibrium points of noncompact abstract economies for $L^*_F$-majorized mappings in FC-spaces, Nonlinear Anal. 72 (2010), no. 1, 65-76.
P. Q. Khanh, N. H. Quan, and J. C. Yao, Generalized KKM type theorems in GFC-spaces and applications, Nonlinear Anal. 71 (2009), no. 3-4, 1227-1234.
S. Park, Remarks on topologies of generalized convex spaces, Nonlinear Funct. Anal. Appl. 5 (2000), no. 2, 67-79.
S. Park, Comments on fixed point and coincidence theorems on multimaps with non-convex or noncompact domains, Varahmihir J. Math. Sci. 6 (2006), no. 1, 15-24.
S. Park, Various subclasses of abstract convex spaces for the KKM theory, Proc. National Inst. Math. Sci. 2 (2007), no. 2, 35-47.
S. Park, Elements of the KKM theory on abstract convex spaces, J. Korean Math. Soc. 45 (2008), no. 1, 1-27.
S. Park, Equilibrium existence theorems in KKM spaces, Nonlinear Anal. 69 (2008), 4352-4364.
S. Park, New foundations of the KKM theory, J. Nonlinear Convex Anal. 9 (2008), no. 3, 331-350.
S. Park, Fixed point theory of multimaps in abstract convex uniform spaces, Nonlinear Anal. 71 (2009), no. 7-8, 2468-2480.
S. Park, Generalized convex spaces, L-spaces, and FC-spaces, J. Global Optim. 45 (2009), no. 2, 203-210.
S. Park, Comments on generalized R-KKM type theorems, Comm. Korean Math. Soc. 25 (2010), no. 2, 303-311.
S. Park, The KKM principle in abstract convex spaces: equivalent formulations and applications, Nonlinear Anal. 73 (2010), no. 4, 1028-1042.
K. Wlodarczyk and D. Klim, Equilibria and fixed points of set-valued maps with nonconvex and noncompact domains and ranges, Nonlinear Anal. 65 (2006), no. 4, 918-932.