Topological algebraic structure on Souslin and Aronszajn lines

摘要

Z. Feng and R.W. Heath proved that any separable linearly ordered space (LOTS) which is a cancellative topological semigroup must be metrizable. In this note, we show that the same holds more generally for CCC LOTS by proving that no Souslin line admits a continuous cancellative binary operation. We also show that no Lindelof Aronszajn line admits such an operation.