- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 3 Issue: 2
- Riemannian manifolds are KKM spaces
Riemannian manifolds are KKM spaces
Authors : Sehie PARK
Pages : 64-73
Doi:10.31197/atnaa.513857
View : 6 | Download : 24
Publication Date : 2019-06-30
Article Type : Other
Abstract :Let (M,g) be a complete, finite-dimensional Riemannian manifold. Based on the fact that any geodesic convex subset of M is a KKM space, we establish the KKM theory on such subsets originated from the Knaster-Kuratowski-Mazurkiewitz theorem in 1929.Keywords : Riemannian manifold, KKM theorem, Abstract convex space, Geodesic convex set