The projective tensor product in a category of topologicalR-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the cartesian closedness of X is related to the monoidal...

The subcategory of a category and product of categories is defined. The inclusion functor is the injection (inclusion) map E ↪→ which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a,b) = HomC(b,b) for any objects a,b of E, are defined. A subcateg...

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

The ability to exchange opinions and experiences online is known as online word of mouth (WOM) and has been shown in the literature to have the potential to impact e-commerce sales. The purpose of this paper is to expand previous findings by empirically evaluating the impact of online WOM attributes and other related factors (e.g. product views, promotion, and category) on e-commerce sales usin...

We determine the Lusternik-Schnirelmann category of projective product spaces introduced by D. Davis. also obtain an upper bound for topological complexity these spaces, which improves estimate given J. González, M. Grant, E. Torres-Giese, and Xicoténcatl.

The aim of this study is to investigate the neural mechanism of extending a brand in a specific product category to other product categories. Facing two sequential stimuli in pairs consisting of beverage brand names (stimulus 1) and product names (stimulus 2) in other categories, 16 participants were asked to indicate the suitability of extending the brand in stimulus 1 to the product category ...