scholarly journals Extension and Selection theorems in Topological spaces with a generalized convexity structure

1993 ◽  
Vol 2 (2) ◽  
pp. 253-269 ◽  
Author(s):  
Charles D. Horvath
Keyword(s):  
Generalized Convexity ◽  
Topological Spaces ◽  
Convexity Structure ◽  
Selection Theorems

scholarly journals Fixed points and selections of set-valued maps on spaces with convexity

2000 ◽  
Vol 24 (9) ◽  
pp. 595-612 ◽  
Author(s):  
Peter Saveliev
Keyword(s):  
Fixed Points ◽  
Generalized Convexity ◽  
Vector Spaces ◽  
Multivalued Maps ◽  
Topological Vector Spaces ◽  
Selection Theorems ◽  
Locally Convex

We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.

scholarly journals Existence of Equilibria for Discontinuous Games in General Topological Spaces with Binary Relations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ji-Cheng Hou
Keyword(s):  
Topological Spaces ◽  
Discontinuous Games ◽  
Binary Relations ◽  
Preference Relations ◽  
Convexity Structure ◽  
Existence Of Equilibria

We provide several results on the existence of equilibria for discontinuous games in general topological spaces without any convexity structure. All of the theorems yielding existence of equilibria here are stated in terms of the player’s preference relations over joint strategies.

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