The physical “continuum” is being modeled as a complex of events interconnected by the relation of extension and forming an abstract partially ordered structure. Operational physical procedures for discerning observable events assume their existence and validity locally, by coordinatizing the informational content of those observable events in terms of real-valued local observables. The localiz...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

The familiar Intermediate Value Theorem of elementary calculus says that if a real valued function f is continuous on the interval [a, b] ⊆ R then it takes each value between f(a) and f(b). As our next result shows, the critical fact is that the domain of f , the interval [a, b], is a connected space, for the theorem generalizes to real-valued functions on any connected space. The Intermediate ...