Symmetric monoidal closed structures in
and objects at in the category of proximity spaces
In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various , , , structures at a point are investigated. Finally, we examine the relationships between the generalized separation...
Tensor products in the category of convergence spaces
Tensor products in the category of topological spaces
The cartesian closed hull of the category of approach spaces
The cartesian closed topological hull of the category of completely regular filterspaces
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The category of uniform frames
The category of uniform spaces as a completion of the category of metric spaces
A criterion for the existence of an initial completion of a concrete category universal w.r.tḟinite products and subobjects is presented. For metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
The completion monad and its algebra
The convergence approach to exponentiable maps.
The duality between lattice-ordered monoids and ordered topological spaces.
The envelope of a subcategory in topology and group theory.
The functor of weakly additive functionals of finite degree.
The monad induced by the hom-functor in the category of topological spaces and its associated Eilenberg-Moore algebras.
The notion of closedness in topological categories
In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated...
The property for finite seminormal functors.
Topological Continuous Convergence.
Topological quasitopos hulls of categories containing topological and metric objects
Topological representations of quasiordered sets.