Mart Abel

On a category of module bundles

It is shown, that the category ℰA(X) ofA-bundles over a topological spaceX is an additive pseudo-Abelian category for each Waelbroeck algebraA.

A generalization of the Serre-Swan-Mallios Theorem

In this paper we prove a generalized version of Serre-Swan-Mallios Theorem for arbitrary Waelbroeck algebras.

On a problem of Bertram Yood

Abstract In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.

THE CENTER OF TOPOLOGICALLY PRIMITIVE EXPONENTIALLY GALBED ALGEBRAS

Let A be a unital sequentially complete topologically primitive exponentially galbed Hausdorff algebra over ℂ, in which all elements are bounded. It is shown that the center of A is topologically isomorphic to ℂ.

Generalization of Segal algebras for arbitrary topological algebras

In the present paper we introduce the definition of a topological Segal algebra, which generalizes most of the earlier known definitions for Segal algebras. We also generalize some results about Segal algebras and algebras of continuous functions vanishing at infinity for the case of topological Segal algebras.

Coincidence of topological Jacobson radicals in topological algebras

Several classes of topological algebras for which the left topological Jacobson radical coincides with the right topological Jacobson radical are described.

ON THE EQUIVALENCE BETWEEN THE CATEGORIES OF CERTAIN BUNDLES AND CERTAIN SHEAVES

In this paper the notion of universal algebra bundle is introduced. We show that several properties of local sections of a certain sheaf hold also for local sections of module bundles and universal algebra bundles. As a main result of this paper, we construct an equivalence between the category of module bundles (or universal algebra bundles) and a certain subcategory of the category of sheaves or a certain subcategory of the category of complete presheaves.

ON THE EQUIVALENCE BETWEEN THE CATEGORIES OF LOCALLY SLICEABLE FIBER SPACES AND SHEAVES OF SETS

In this paper we prove that the category of locally sliceable fiber spaces over the fixed topological space X and the category of sheaves of sets over the same topological space X are equivalent.

GENERALIZATION OF THE SERRE-SWAN-MALLIOS THEOREM FOR SHEAVES AND PRESHEAVES

In the present paper we give the versions of generalized Serre-Swan-Mallios Theorem for sheaves and presheaves. In order to do it, we introduce new classes of sheaves and presheaves, called suitable sheaves and suitable presheaves.

On the sheaf of extendible ideals of topological algebras

In this paper a new sheaf for topological algebras, called the sheaf of extendible ideals, is introduced. It is shown that the sheaf space of this sheaf is uniformizable but not complete in general.