Topological Algebraic Structure on Souslin and Aronszajn Lines
نویسندگان
چکیده
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 Lindelöf Aronszajn line admits such an operation.
منابع مشابه
Souslin trees and successors of singular cardinals
The questions concerning existence of Aronszajn and Souslin trees are of the oldest and most dealt-with in modern set theory. There are many results about existence of h+-Aronszajn trees for regular cardinals A. For these cases the answer is quite complete. (See Jech [6] and Kanamory & Magidor [8] for details.) The situation is quite different when A is a singular cardinal. There are very few r...
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