Volume 10, Issue 2, pages 76-99
In this paper I inquire into the applicability of topological structures in the mathematical modeling of certain quantum situations and attempt an interpretation, on the level of metatheory, of phenomena associated with the time evolution of quantum processes and the individuality of quantum objects upon observation. Accordingly the paper engages, on the one hand, in an epistemologically oriented discussion of the merits of topological approaches concerning natural science in general and certain questions of quantum theory in particular, and on the other, in an elaboration of a proper topological structure to deal with the mathematical aspects of an open question of the theory of quantum histories, the latter as developed mainly by C. J. Isham and co. On this motivation a brief discussion concerning the topological nature of the Bohm-Aharonov effect is thought to be in order. Overall the primary focus is to discuss the relevance of topology, as a pure mathematical theory of structures, with the quantum context and in particular of the quantum histories processes over temporal points and continuous time intervals.