Abstract
This chapter discusses the study of the properties of Borel subsets of metric spaces. The main result of the isomorphism theorem asserts that Borel subsets of complete separable metric spaces are isomorphic if they have the same cardinality. For any separable metric space X, one writes X0 for the space of all functions x from the positive integers to X. A point x ε X0 can be expressed as a sequence (x1, x2…), where each xn ε X. The same symbol is used to denote the space X as well as the Borel space of which it is the underlying set. The countable product of the space consisting of two points 0 and 1 is denoted by M. M is the space of sequences of 0s and ls. M is a compact metric space in its natural (product) topology.
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 callDisclaimer: 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.
