Category Of Convergence Spaces Research Articles

Partial actions on convergence spaces

Abstract Continuous partial actions and continuous enveloping actions are investigated in the category of convergence spaces. Product and quotient constructions are considered. Further, it is shown that a continuous partial action on a convergence space can be extended to a continuous partial action on a compactification of the convergence space.

Gähler's neighborhood condition for lattice-valued convergence spaces

We generalize a neighborhood condition from the category of convergence spaces to the category of lattice-valued convergence spaces. For a space in the category of convergence spaces, this condition is equivalent to being a topological space. It turns out that there are two meaningful generalizations of this condition to the category of lattice-valued convergence spaces. The first one guarantees that a space in a certain subcategory is a lattice-valued topological space. The other one is a levelwise condition which is equivalent to a generalization of Fischer's diagonal condition. The latter generalization is preserved under the embedding of the categories of convergence approach spaces and of probabilistic limit spaces into the category of lattice-valued convergence spaces.

Convergence semigroup actions: generalized quotients

Continuous actions of a convergence semigroup are investigated in the category of convergence spaces. Invariance properties of actions as well as properties of a generalized quotient space are presented

A note on separation and compactness in categories of convergence spaces

<p>In previous papers, various notions of compact, T<sub>3</sub>, T<sub>4</sub>, and Tychonoff objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the categories of filter and local filter convergence spaces as well as to examine how these various generalizations are related.</p>

Regularity in fuzzy convergence spaces

The notions of regularity and weak regularity are introduced in the category of fuzzy convergence spaces, and each is shown to be an extension of regularity with respect to the embedding functor from the category of convergence spaces. Moreover, the category whose objects are weakly regular fuzzy spaces is topological and thus initial and final regular structures exist. The relationship between regularity and a diagonal condition is given.

Foundational Isomorphisms in Continuous Differentiation Theory

We provide an elementary proof of existence for the Foundational Isomorphism in each of the categories of convergence spaces, compactly generated topological spaces and sequential convergence spaces. This isomorphism embodies the ‘germ’ of differentiation and its inverse the ‘germ’ of integration.

A dual adjointness on partially ordered topological spaces

The spectral dual adjoint between the mixed category X of the category of partially ordered sets and the category of convergence spaces and that of distributive lattices with 0 and 1 formed over X has been constructed by Hong and Nel. They have extended the Priestly duality. In this paper, another spectral dual adjoint has been constructed by the use of simple topological convergences, rather than by the use of the structures of convergence spaces. It is shown that this adjunction is an extension of the Banaschewski duality. Further, another kind of Priestly type duality is obtained.

Completion Functors for Categories of Convergence Spaces II. Embedding of Separated Acceptable Spaces into their Completion

Completion Functors for Categories of Convergence Spaces II. Embedding of Separated Acceptable Spaces into their Completion

A cartesian closed category for topology

By replacing sequences by sets in definitions of Fréchet and Urysohn, one obtains the definition of an L ∗ space. The category of L ∗ spaces properly contains the category of topological spaces, it is cartesian closed, and it has other properties which make it convenient for topology. The category of L ∗ spaces is properly smaller than the category of convergence spaces (Limesräame) of Cook and Fischer, but properly larger than the category of epitopological spaces of Antoine.

Solid convergence spaces

The category of solid convergence spaces is introduced, and shown to lie strictly between the category of all convergence spaces and that of pseudo-topological spaces. A wide class of convergence spaces, including the c-embedded spaces of Binz, is then characterized in terms of this concept. Finally, several illustrative examples are given.

On a marinescu structure onC (X)

The purpose of this note is to introduce a natural Marinescu structure [7] (an inductive limit of locally convex topological vector spaces in the category of convergence spaces) on C(X) , where C(X) denotes the IR-algebra of all continuous real-valued function on a completely regular topological space X. The structure in question is closely related to Cc(X) , the algebra C(X) endowed with the continuous convergence structure [1].