الفهرس 
acknowledgmentOnly 14 pages are availabe for public view
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Abstract
There is no doubt that one can say that topology is the science of the future.
As a result of the communication revolution, the development has increased,
the culture have approached and nations have interfered ; and this led to the
need of mathematical models deals though approaching view not similar view.
Topology and its applications occupies the interest of many researching
centers in the advanced world; for example Hokkaido University, in Japan,
has established a cent er known as Center of Excellence ”C.O.E”. from their
point of view, excellence is the use of topology ,so that they have made its title
”Topological Sciences and Technology” ;that is because topology is required
not only for mathematics and physics but also for biology , network theory ,
information theory, and economy, and mathematics development.
The concept of general topological space became more important in the
beginning on the 21th century; the applications ,which depending on general
space , has achieved may achievements.
General topology has been considered the interface to understand topology
science , moreover the base of general topology is the topological space is the
topological space, which has been considered a representation of universal
space in general, and geometric shape in spacial , also the mathematical anal-
ysis concepts . Recently , the general topology has become the appropriated
frame for every collection connected by relations .It should be noted that the
generation of topology by relations and the representation of topological con-
cepts via relations will narrow the gab between topologist and those who are
interested in applications of topology in their fields . Relations were used in
the construction of topological structures in several fields such as , rough set
theory [14, 16],digital topology [23, 24] , biochemistry [25], biology [26], gen-
eral view of space time [7] and structural analysis only in almost all branches
of mathematics, but also in many real life applications.
Although this wide range of application fields for topologies generated by
relations, the use of topological results and concepts is still limited on the
preliminary notions in general topology . So we choose this line aiming to fill
the gap between topologist and applications.
This thesis, consisting of for chapters are following that:
We introduce Chapter 1 to review some basic concepts of topological
space and some definitions related with this work .In addition, we present a
review of the Pawlak approximation space constructed from an equivalenc.e