Authors: Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On a cohomology theory based on hyperfinite sums of microsimplexes
Journal: Pacific Journal of Mathematics
Volume: 128
Issue: 1
First page: 201
Last page: 208
Issue Date: 1-Jan-1987
Rank: M23
ISSN: 0030-8730
DOI: 10.2140/pjm.1987.128.201
In this note we investigate a cohomology theory H#(X, G), defined by M. C. McCord, which is dual to a homology theory based on hyperfinite chains of miscrosimplexes. We prove that if X is a locally contraction, paracompact space then H#(X, G) ≃ Hč#(X, Hom(*Z, G)) where Hč# is the Čech theory. Nonstandard analysis, particularly the Saturation Principle, is used in this proof in essential way to construct a fine resolution of the constant sheaf X × Hom(*Z, Z). This gives a partial answer to a question of McCord. Subsequently, we prove a proposition from which it is deduced that Hom(*Z, Z) = {0} i.e. H#(X, Z) = {0} if X is paracompact and locally contractible. At the end we briefly discuss a related cohomology theory which is obtained by application of the internal (rather than external) Hom(·, G) functor.
Publisher: MPS

Show full item record


checked on Dec 6, 2022

Page view(s)

checked on Dec 6, 2022

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.