A = a Matching Points and Identity

Recently introduced versions of the Borsuk-Ulam theorem (BUT) state that a feature on a n-manifold projects to two features with matching description onto a n+1 manifold (Peters, 2016; Peters and Tozzi, 2016a, 2016b; Tozzi, 2016; Tozzi and Peters, 2016a, 2016b). Starting from this rather simple “abstract” claim, a fruitful general framework has been built, able to elucidate disparate “real” physical and biological phenomena, from quantum entanglement (Peters and Tozzi, 2016c), to brain activity (Peters et al., 2016, 2017; Tozzi and Peters, 2016a, 2016b, 2017), from gauge theories (Tozzi et al., 2017) to prebig bang scenarios (Tozzi and Peters, 2016c). Summarizing this novel topological approach, we may state what follows: if you take into account projections among functional or real dimensions, you achieve a system of mappings that fit very well with experimental results and are able to assess countless systems in far-flung scientific branches. One of the main concerns of such a topological approach to systems features is that it talks in rather general terms, leaving apart the peculiar features of individuals and of single physical and biological processes.