For every natural number n, the multibrot set of power n is locally connected. The multibrot set of power n is defined as the set of all complex parameters c for which the orbit of 0 under iteration of the map z↦zn+c does not escape to infinity; equivalently, it is the set of all c∈C such that for every non-negative integer k, the k-fold iterate of z↦zn+c applied to 0 has modulus at most 2(n−1)−1 when n≥2. A topological space is locally connected if every point has a neighborhood base consisting of connected open sets. Prove that for every n∈N, the multibrot set of power n, equipped with the subspace topology from C, is a locally connected space.