[2] **viXra:1506.0184 [pdf]**
*submitted on 2015-06-25 19:16:39*

**Authors:** a. a. Salama

**Comments:** 5 Pages.

Since the world is full of indeterminacy, the neutrosophics
found their place into contemporary research. The fundamental
concepts of neutrosophic set, introduced by Smarandache
in [30, 31, 32] and Salama et al. in [4-29]. In Geographical
information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some classes of neutrosophic crisp nearly open sets are investigated and some applications are given.Finally we generalize the crisp topological and intuitioistic studies to the notion of neutrosophic crisp set. Possible applications
to GIS topological rules are touched upon.

**Category:** Topology

[1] **viXra:1506.0139 [pdf]**
*replaced on 2015-07-11 05:48:01*

**Authors:** Luis Sancho

**Comments:** 32 Pages.

We expand the holographic principle to explain the nature of the universe and all its fractal 2-manifold organisms. The simplest explanation of the complex universe departs from the holographic principle: information, form is bidimensional. Because all what we perceive is the 'cover' of things, its membranes. Thus in a 2-manifold, in a bidimensional world there are only 2 topologies, which correspond to the main parts of any system, the lineal, energetic and spherical informative dimensions or motions (since energy is just space in motion and time information cyclical form in motion). And its 'wavelike combinations, exi. And we shall call energy, to th expansive motions, which form limbs, often with hyperbolic topology (bilateral). And we shall call information to the implosive vortices, which form particles and heads, often of spherical geometry. And the space between them the 3 membrane-topology of the universe, its body wave, the ExI part of the system. Thus all what exists are polar systems, with 'energy fields/limbs' and informative heads/particles, exchange energy and information creating a 3rd element, 'waves-bodies'.
We use the formalism to unify all disciplines of human knowledge, showing all its species display 5 isomorphisms, derived of the 3 topologic varieties:
- isomorphism of 3 finite, diffeomorphic dimensions of space
- isomorphism of 3 time-ages/states, past- young energy, liquid balanced present and solid, future, wrinkled age
- isomorphism of 3 space-time topologies, energy, iteration and information
- isomorphism of 3 hierarchies of organisation, the quantum/cellular, i-ndividual/human and social/cosmic scale
- isomorphism of 3 actions, energy feeding, reproductive iteration and informative gauging.
Whereas the 4 dimensional universe is the holographic intersection of 2-manifold membranes, and the Whole Universe a fractal sum of all of them

**Category:** Topology