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Abstract For a long time, most mathematicians and engineers believed that topology is an abstract mathematical branch which is far from application fields. But now this assertion is not acceptable because of the wide range of topological applications. An example for the importance of topology in technology applications: Hokkaido University in Japan constructed a center of Excellency COE for ”Topological sciences and technology” The following is a part from the introduction written by the leader of the center: ”This center will create a new scope and an innovative field of study from the perspective of topology, a universal concept that is applicable across a -wide range of fields. Incorporating mathematical science, applied physics, instrumentation and information technology, materials science, life science, and economics, we aim to build a true center of excellence for original and interdisciplinary research and education, both basic and applied” The following diagram taken from the web site of COE |