Precompactness and total boundedness in products of metric spaces.
Recently, Rim and Teply , using the notion of -exact modules, found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod of all unitary left -modules over an associative ring with identity. Some relations between -torsionfree and -exact covers have been investigated in . The purpose of this note is to show that if is Goldie’s torsion theory and is a precover class, then is a precover class whenever...
We investigate the category of product preserving bundle functors defined on the category of fibered fibered manifolds. We show a bijective correspondence between this category and a certain category of commutative diagrams on product preserving bundle functors defined on the category ℳ f of smooth manifolds. By an application of the theory of Weil functors, the latter category is considered as a category of commutative diagrams on Weil algebras. We also mention the relation with natural transformations...
The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given.
The paper introduces Cartesian products in categories without uniqueness of cod and dom. It is proven that set-theoretical product is the product in the category Ens [7].