Riemannian manifolds are KKM spaces

Open Access

Original research article

Author(s):

Sehie Park^a,b

^aThe National Academy of Sciences, Republic of Korea, Seoul 06579, Korea
^bDepartment of Mathematical Sciences, Seoul National University, Seoul 08826, Korea

Advances in the Theory of Nonlinear Analysis and its Applications 3(2), 64-73.

Received: November 11, 2018

Accepted: February 14, 2019

Published: May 3, 2019

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.

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APA Style

Park, S. (2019). Riemannian manifolds are KKM spaces. Advances in the Theory of Nonlinear Analysis and its Application, 3(2), 64-73.