##plugins.themes.bootstrap3.article.main##
Abstract
It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups with open shifts are topological groups and to give a sufficient condition under which a locally compact monothetic topological semigroup is a compact topological group.
##plugins.themes.bootstrap3.article.details##
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.
Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.