%0 Journal Article
%T On locally extremal functions on connected spaces
%A T. Banakh
%A M. Vovk
%A M. R. Wojcik
%J Mathematics
%D 2008
%I arXiv
%X We construct an example of a real-valued continuous non-constant function $f$ defined on a connected complete metric space $X$ such that every point of $X$ is a point of local minimum or local maximum for $f$. The space $X$ is connected but fails to be separably connected.
%U http://arxiv.org/abs/0811.1771v1