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The main subject of our study is the application of topology in physics. During our studies we notice that first we should have a deep understanding of the concept of phase in order to understand the application of topology in physics. The Concept of phase itself is one the most important concepts in Condensed Matter Physics .This concept is also very fundamental and the term phase has other applications in other areas of science. Thus, if we get a deep understanding of this Concept we are also able to understand other areas of science well.
To talk about this concept, we first discuss some backgrounds to make our minds ready then we will discuss the main concept : The Phase .
What we did first during our study was to define something we call Layer. After the introduction of the concept of Layer we talked about the layers themselves which one of their characteristics is that some of them lay over others. Another characteristic of this layers is that some of them, in reality, are prior to others.
But what are these Layers? What are the criterions of choosing the layers? What is the relation between these layers and the phase? We answered these questions in our study and use these concepts to define phase and at last we discuss the applications of topology in physics .