Category theorems

Ideal Banach Category Theorems and Functions

Based on some earlier findings on Banach Category Theorem for some “nice” σ-ideals by J. Kaniewski, D. Rose and myself. I introduce the h operator (h stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of h...

HSP Type Theorems in the Category of Posets

As a computer science application of our techniques we may take the action logic of [Pratt, 1990]. Action logic is a finitely based equational theory conservatively extending the equational theory of regular expressions. An action algebra (model of action logic) is implicitly partially ordered via a ≤ b just when a + b = b . However a + b plays no other essential role in action logic, and may b...

Category of Polygroup Objects

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.