Abstract
This chapter presents a proof that every semigroup S with identity element can be represented by the semigroup Q(M) of all quasi-local homeomorphisms of a metric space M into itself. The semigroup Q(M) of all quasi-local homeomorphisms seems to be the most suitable to replace the group of all autohomeomorphisms A(M). The chapter proves the existence of a semigroup S such that there is no Hausdorff-space H such that S is isomorphic to the semigroup of all local homeomorphisms of H into itself. Neither can S be isomorphic to the semigroup of all open continuous mappings of H into itself. f : X → Y is a local homeomorphism if for each x ∈ X there exists an open set O, x ∈ O such that f | O is a homeomorphism of O onto f(0).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: General Topology and Its Relations to Modern Analysis and Algebra 2
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
