الفهرس 
Survey on Related TopicsOnly 14 pages are availabe for public view
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Abstract
Topology is one of the most significant branches of mathematics, which plays
a crucial part in real life applications. In this thesis, we use a graph theory and
rough set theory to generate new forms of nano topological structures from any
simple directed graph. Moreover, a digraph model of a human blood circulation is
introduced and nano topological spaces are generated. Some definitions of separation
axioms depended on topological structures of graphs are studied in both the
digraph of the heart and any other simple directed graph. Simplicial complexes
also are played an important role in an algebraic topology. They are geometric
objects that can be created and used in real-world situations. A universal set of
any simplicial complexes are introduced as a set of vertices, edges, faces, tetrahedrons,
and so on. A betweenness relation on any simplicial complex is defined and
some of its topologies are studied. Matroids are offered as abstract extensions to
the linear independency in vector spaces and cycles in graphs. They have strong
theoretical foundations and a wide range of applications. In this thesis, we make
connections between simplicial complexes, matroid theory and a rough set theory
to generate new types of matroids called simplicial matroids. Some of these
simplicial matroids are generated from any simplicial complex by defining special
kind of matrices on it. Some of them are generated by defining special kinds of
relations on the simplicial complex such as equivalence relation and order relation.
Moreover, we study some of matroidal characterizations of these simplicial
matroids.