The rise and fall of MC-spaces

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  • Sehie Park


KKM theorem, Fan's 1961 KKM lemma, G-convex space, mc-space, L-space, abstract convex space, (partial) KKM space.


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 justications. Later he insisted that his mc-spaces are the same as L-spaces. Hence his study on mc-spaces is useless 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.




How to Cite

Sehie Park. (2022). The rise and fall of MC-spaces. Results in Nonlinear Analysis, 4(1), 21–33. Retrieved from