Uniform Lipschitz-connectedness and metric convexity
نویسندگان
1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.
2 Department of Mathematics and Applied Mathematics University of the Western Cape South Africa
doi
10.48308/cgasa.2024.235538.1489چکیده
In this paper we continue with our study of uniformly Lipschitz-connected metric spaces. We obtain further properties of uniformly Lipschitz-connected metric spaces and then obtain a generalisation of a result due to Edelstein. In addition, we show that for a proper Lipschitz-connected metric space, $L_d = 1$ precisely when $X$ is convex, which leads us to conjecture that $L_d$ is a kind of measure of convexity in a proper Lipschitz-connected metric space. We provide some examples to corroborate our conjecture.
