Abstract
In this article we give a description of a certain new homology theory on fairly wide categories of topological spaces, as well as a survey of papers concerning this construction. In contrast to the Aleksandrov-Äech homology theory this theory satisfies all the Eilenberg-Steenrod axioms, including exactness. In the end it turns out to be equivalent to the Steenrod homology theory and very close to the Borel-Moore homology theory, being isomorphic to it when the coefficient module is finitely generated (without this condition the Borel-Moore theory is not well-defined). We show that many results of the Borel-Moore theory take their most definitive and natural form in the homology theory under discussion. The methods of sheaf theory, which are used in the Borel-Moore homology theory, can be applied just as effectively in our case.
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 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.
