The rise and fall of L-spaces

Authors : Sehie PARK

Pages : 152-166

Doi:10.31197/atnaa.786151

View : 15 | Download : 6

Publication Date : 2020-08-31

Article Type : Research Paper

Abstract :For a quite long period, the so-called L-structure or L-spaces have been studied by some authors. They have several trivial misconceptions such as their L-spaces extend the well-known generalized convex insert ignore into journalissuearticles values(G-convex); spaces. In order to clarify this matter and others, we show that our KKM theory on abstract convex spaces improves typical results in L-spaces. Main topics in this paper are related to extensions of the Himmelberg fixed point theorem. Since such studies are beyond of L-spaces, we cordially claim that now is the proper time to give up the useless study on L-spaces and their variants FC-spaces.
Keywords : FC space, L space, Fixed Point Theorem Partial, KKM space, Abstract convex space, KKM theorem, Multimap classes KC, KO