Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(1): 305-320

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.305

Copyright © The Korean Mathematical Society.

Applications of results on abstract convex spaces to topological ordered spaces

Hoonjoo Kim

Sehan University

Abstract

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

Keywords: abstract convex space, KKM map, generalized KKM, generalized $\gamma$-quasiconvexity, maximal elements, topological semilattices with path-connected intervals, collectively fixed point

MSC numbers: 47H10, 47H04, 52A07, 54C60, 54H25