title: The topology of perceptive functions as a corollary of the theorem of existence in closed spaces.
abstract: The capability for a system of perceiving both outer objects and an inner self are two fundamental features of abstract mathematical objects endowed with the properties of topologically closed sets. Such structures exist upon intersection of topological spaces owning different dimensions. Then, the theorem of Jordan-Veblen provides their capability of being observable, while the theorems of Brouwer and of Banach-Caccioppoli provide two kinds of fixed points which account for the properties of so-called right and left brain functions. Fixed points account for the biological 'self', and the system provides theoretical justification for the existence of brain structure/function relationships, including memory, emotion, and respective characteristics of right and left hemispheres. Hence, an abstract topological reasoning based on set properties, provides evidence that the observer's function directly infers from the phenomenon of existence and that it belongs to the same mathematical system as the property of being observable. Order relations are raised from equivalence relations by Poincaré groups, upon mappings on the sets of functions and related homotopic transformations in sequences of intersections. Therefore, time is a construction of abstract brain functions, and a living organism just fills the system with appropriate molecular structures.
authors.affiliation: Université d'Avignon, Biomathématique et Toxicologie, Faculté des Sciences, Avignon, France.
authors.forename: M
authors.initials: M
authors.lastname: Bounias
authors.forename: A
authors.initials: A
authors.lastname: Bonaly
mesh_terms: D005075:Biological Evolution; D001921:Brain / Q000502:physiology; D006801:Humans; D008128:Logic; D008433:Mathematics; D008960:Models, Psychological; D010465:Perception; D010684:Philosophy; D011601:Psychophysics; D013997:Time Factors