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...

Abrams’ theorem describes a necessary and sufficient condition for the closedness of a linear image of an arbitrary set. Closedness conditions of this type play an important role in the theory of duality in convex programming. In this paper we present generalizations of Abrams’ theorem, as well as Abrams-type theorems characterizing other properties (such as relatively openness or polyhedrality...

Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we start from the failures presented by the classical Banach manifolds approach and we will review the m...

We investigate the frame properties and closedness for the shift invariant space

The aim of this note is to study local and global Seshadri constants for a family of smooth surfaces with prescribed polarization. We shall first observe that given α being smaller than the square root of the degree of polarization, the set of local Seshadri constants in the range (0, α] is finite. This in particular implies that the square root of the degree of polarization is the only possibl...

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...

We prove the Existential Closedness conjecture for differential equation of j j -function and its derivatives. It states that in a differentia...