A regular separable first-countable countably compact space is called a Nyikos space. A space \(X\) is called \(\mathbb{R}\)-rigid if any continuous real-valued function on \(X\) is constant. Under MA we construct an \(\mathbb{R}\)-rigid Nyikos space. This way we answer a few questions of Tzannes and extend results of Ciesielski and Wojciechowski.
This is a joint work with Zdomskyy.