Duality, localization and completion

Amodal completion and localization

In a three-line vernier acuity task, a central line was localized between two aligned line segments. Accuracy did not improve when the segments formed a unified amodally completed percept. In a two-line vernier acuity task, a line was localized below a target line placed next to a physically segmented flank stimulus. Shifts in mean points of subjective equality suggested that amodally completed...

Fibrewise Localization and Completion

The behavior of fibrewise localization and completion on the classifying space level is analyzed. The relationship of these constructions to fibrewise joins and smash products and to orientations of spherical fibrations is also analyzed. This theory is essential to validate Sullivan's proof of the Adams conjecture. In Sullivan's beautiful proof of the Adams conjecture [20], perhaps the crucial ...

Localization and String Duality

According to string theorists, String Theory, as the most promising candidate for the grand unification of all fundamental forces in the nature, should be the final theory of the world, and should be unique. But now there are five different looking string theories. As argued by the physicists, these theories should be equivalent, in a way dual to each other. On the other hand all previous theor...

Localization and Completion in Homotopy Theory

Connecting the profinite completion and the canonical extension using duality

We show using duality and category theory that the profinite completion  of a bounded distributive lattice expansion A is a homomorphic image of the canonical extension Aσ . Moreover the natural mapping μ : A →  can be extended to a surjection ν : Aσ ! Â.