Quotient-topological completions and hulls of concrete categories

Cotopological completions and hulls of concrete categories

Tower extension of topological constructs

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

On Countable Completions of Quotient Ordered Semigroups

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

p-TOPOLOGICAL CAUCHY COMPLETIONS

The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular,p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and onl...

Met-like categories amongst concrete topological categories

When replacing the non-negative real numbers with their addition by a commutative quantale V, under a metric lens one may then view small V-categories as sets that come with a V-valued distance function. The ensuing category V-Cat is well known to be a concrete topological category that is symmetric monoidal closed. In this paper we show which concrete symmetric monoidalclosed topological categ...