TITLE: Who is credited with the creation/invention of the cup product?
QUESTION [11 upvotes]: Who is credited with the creation/invention of the cup product?  Wikipedia gives credit to several but I wasn't able to confirm.

REPLY [10 votes]: W. S. Massey gives a rather detailed account in his essay, "A history of cohomology theory" (in History of Topology, edited by I. M. James, North Holland, 2006).  The initial idea was due to Alexander and Kolmogoroff, apparently simultaneously and independently, but there were some "bugs" in the original version.  Čech and Whitney, in separate papers, cleaned up the definition (Čech for finite simplicial complexes, Whitney more generally for finite cell complexes).