The author considers equivalence direlations and the corresponding quotients of textures, using the interior relation on the texture as a tool in this investigation. A close relationship with surjective difunctions is shown, and the notions of quotient ditopology and quotient difunction are defined and studied. Finally, the existence of a T0 reflection on the category dfDitop is established.

this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...

This paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated Drading functions. The resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. Interrelations between graded ditopologies and ditopologies on textur...

We show that on a process graph defined by 1-semaphores, the space of directed paths (or dipaths) deformation retracts to a discrete set correlated by homotopy class relative to endpoints. This result extends to the set of ‘fastest executables’ (time-optimal dipaths). These results are obtained via techniques from cat(0) geometry and spaces of nonpositive curvature. keywords: CAT(0), nonpositiv...

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander {v S}ostak in cite{BS}. In this paper, the authors generalize the structure of diuniformity in ditopological texture spaces defined in cite{OB} to the graded ditopological texture spaces and investigate graded ditopologies generated by graded diuniformities. The autors...

John Baez, Computations and the periodic table By now there is an extensive network of interlocking analogies between physics, topology, logic and computer science, which can be seen most easily by comparing the roles that symmetric monoidal closed categories play in each subject. However, symmetric monoidal categories are just the n = 1, k = 3 entry of a hypothesized ”periodic table” of k-tupl...