Sequentially Compact Cancellative Topological Semigroups - Some Progress

Abstract

Some results of Mukherjea and Tserpes are generalized by showing that any sequentially compact, cancellative topological semigroup is a topological group. Hence, any countably compact, cancellative topological semigroup with any additional condition that would imply sequential compactness is also a topological group. Finally, it is shown that any omega-bounded, cancellative topological semigroup is also a topological group.