Abstract
This chapter presents a survey of results concerning the covering dimension of general topological spaces without any separation axiom, together with some related results. There are several results in homotopy theory of CW-complexes that require dimensional restriction. One of the fundamental theorems in dimension theory is the sum theorem. The small inductive dimension does not satisfy the finite sum theorem even in metric spaces. For any topological space X, three kinds of dimension functions can be defined: (1) the small inductive dimension ind X, (2) the large inductive dimension Ind X, and (3) the covering dimension dim X.
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.
