# Topology

## 1701 Submissions

[2] **viXra:1701.0649 [pdf]**
*submitted on 2017-01-28 01:09:57*

### Matching Points and Identity

**Authors:** Arturo Tozzi

**Comments:** 3 Pages.

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. 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, to brain activity, from gauge theories to pre- big bang scenarios. 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. In order to tackle this issue, in this brief note we ask: what does it mean “matching description”? has matching description anything to do with “identity”?

**Category:** Topology

[1] **viXra:1701.0519 [pdf]**
*submitted on 2017-01-17 00:26:31*

### MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem

**Authors:** W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

**Comments:** 278 Pages.

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset matrix special type of matrix topological spaces. Likewise using MOD interval natural neutrosophic subsets matrices semigroups we can build MOD interval natural neutrosophic matrix subset special type of topological spaces. We also do build MOD subset coefficient polynomial special type of topological spaces. The final chapter mainly proposes several open conjectures about the validity of the Kakutani’s fixed point theorem for all MOD special type of subset topological spaces.

**Category:** Topology