An extension theorem for sober spaces and the Goldman topology

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

Baire Spaces, Sober Spaces

In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:

The Hopf Extension Theorem for Topological Spaces

Sober Spaces and Continuations

A topological space is sober if it has exactly the points that are dictated by its open sets. We explain the analogy with the way in which computational values are determined by the observations that can be made of them. A new definition of sobriety is formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but, for topological spaces, this...

An Extension of the Marcinkiewicz Interpolation Theorem to Lorentz Spaces

V J o v J t f(y) ) " ) 7 V J o ~ ) • Third, previously open questions concerning the Marcinkiewicz Theorem are settled by showing our result is best possible. Consider complex-valued, measurable functions ƒ defined on a measure space (ikf, m). The distribution function of ƒ is defined by (2) X(y) = X/GO =m{xeM:\ ƒ(*) | > y}, y > 0. X(y) is nonincreasing and continuous from the right. The noninc...