TY - JOUR T1 - The rise and fall of MC-spaces AU - Park, Sehie PY - 2021 DA - March DO - 10.53006/rna.852462 JF - Results in Nonlinear Analysis JO - RNA PB - Erdal KARAPINAR WT - DergiPark SN - 2636-7556 SP - 21 EP - 32 VL - 4 IS - 1 LA - en AB - In 1994, Llinares introduced mc-spaces and began to study KKM theoretic results on them. Since 1998, he became an L-space theorist and repeated to claim that his mc-spaces generalize G-convex spaces without any justifications. Later he insisted that his mc-spaces are the same as L-spaces. Hence his study on mc-spaces isuseless now as the L-space case shown by our previous works. The present article is a continuation of our previous works on L-spaces and concerns with the rise and fall of mc-spaces. This paper will be an important record for the history of the KKM theory. KW - KKM theorem KW - Fan's 1961 KW - G-convex space KW - KKM lemma KW - (partial) KKM space KW - mc-space KW - abstract convex space KW - L-space CR - [1] H. 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Park, Several episodes in recent studies on the KKM theory, Nonlinear Anal. Forum 15 (2010) 13–26. CR - [30] S. Park, New generalizations of basic theorems in the KKM theory, Nonlinear Anal. 74 (2011) 3000–3010. CR - [31] S. Park, Remarks on simplicial spaces and L* -spaces of Kulpa and Szymanski, Comm. Appl. Nonlinear Anal. 19(1) (2012) 59–69. CR - [32] S. Park, A review of the KKM theory on pi A -spaces or GFC-spaces, Advances in Fixed Point Theory 3(2) (2013) 353–382. CR - [33] S. Park, A unified approach to generalized KKM maps, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 55(1) (2016) 1–20. CR - [34] S. Park, The rise and fall of L-spaces, Adv. Th. Nonlinear Anal. Appl. 4(3) (2020) 152–166. CR - [35] S. Park, The rise and fall of L-spaces, II, Adv. Th. Nonlinear Anal. Appl. 5(1) (2021) 1–15. CR - [36] S. Park, Revisit to Generalized KKM maps, to appear. CR - [37] S. Park and H. Kim, Admissible classes of multifunctions on generalized convex spaces, Proc. Coll. Natur. Sci. 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