M-4 is regular-closed

For each n >= 2, we investigate a family of iterated function systems which is parameterized by a common contraction ratio s 2 D fs 2 C V 0 < js j < 1 g and possesses a rotational symmetry of order n. Let M n be the locus of contraction ratio s for which the corresponding self-similar set is connected. The purpose of this paper is to show that Mn is regular-closed, that is, int Mn DMn holds for n 4. This gives a new result for n D 4 and a simple geometric proof of the previously known result by Bandt and Hung [Fractal n-gons and their Mandelbrot sets. Nonlinearity 21 (2008), 2653-2670] for n >= 5.