$lg$-topology

$LG$-topology

In this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎We study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

Moduli stacks Lg,S

This paper is a sequel to the paper by A. Losev and Yu. Manin [LoMa1], in which new moduli stacks of pointed curves were introduced. In particular, the structure sections are divided into two groups, and the sections of the second group are allowed to intersect. The homology of these stacks form components of extended modular operad which will be further studied in [LoMa2]. In this paper the ba...

LG-PACKAGE: New Frontier

(LG) tools, introduced first in 2004. LG is a type of game theory that generates best strategies for all sides in a conflict in real time. The paper describes the main advanced features of the versions (through Version 3.7) of LG-PACKAGE released gradually from 2004 through 2010. These releases converted LG-PACKAGE into the software of industrial strength applicable to the wide scope of defense...

Linguistic Geometry Tools: LG-PACKAGE

Linguistic Geometry Tools: LG-PACKAGE

Topology coloring

The purpose of this study is to show how topological surfaces are painted in such a way that the colors are borderless but spaced with the lowest color number. That a surface can be painted with at least as many colors as the condition of defining a type of mapping with the condition that it has no fixed point. This mapping is called color mapping and is examined and analyzed in differe...