Abstract
It is the purpose of this note to show that there exists an infinite Boolean algebra which has no proper automorphisms.' We shall construct a simply ordered set S, introduce a topology on this set in the usual manner, the so-called interval topology determined by the ordering relation,2 and prove that S is a compact zero-dimensional Hausdorff space and that the only homeomorphism on S onto S is the identity mapping. It is well known3 that the group of automorphisms of the set-field 3 consisting of all open and closed subsets of S is isomorphic to the group of all homeomorphisms on S onto S, whence it follows that B3 has no proper automorphisms. Consider a simply ordered set S with at least two elements. By the interval topology on S we mean the topology which has as a subbasis for open sets, the family of all sets UCS such that either
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