(untitled)
The automorphisms of the lattice L(V_∞ ) have been completely characterized. However, the question about the number of automorphisms of the lattice L^ * (V_∞ ) has been open for almost thirty years. We use some of our recent results about the structure of L^ * (V_∞ ) to answer questions related to automorphisms of L^ * (V_∞ ). We prove that any finite number of partial automorphisms of filters of closures of quasimaximal sets can be extended to an automorphism of L^ * (V_∞ ). As a corollary we obtain that closures of quasimaximal sets of the same type are elements of the same orbit in L^ * (V_∞ ). , journal=Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, year=2009, month=Dec., pages=183–191