Abstract
We show that for a fixed space X and any sufficiently highly connected space A(conn(A)>dim(X)) is more than enough), the Lusternik–Schnirelmann category of products with X is remarkably stable with respect to changes in the second variable: cat(X×A)= cat(X×(A⋊B)) for all spaces B. Taking X=Sn leads to a closure property for the collections of spaces which do or do not satisfy the Ganea condition cat(Sn×A)=1+cat(A).
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