Conclusion

After introducing the concept of layer, we described the reality in terms of layers that lay over each other and together form the universe.

Then we introduced two fundamental layer : Space and Matter.

Space and matter together form our material system.

We briefly talked about the theories of space and matter and gave a definition of them using the method of definition of things that we introduced.

After that we talked about the system and its properties and discussed some important properties in detail.

We defined phase as a collection of some determined appropriate properties.

Then we discussed the procedure of studying the system in detail.

We discussed an example of a new phase of matter and phase transition which we called topological phase of matter and topological phase transition.



By have a general look to what we discussed, we see that the study of the systems needs a deep and vast background in many fields including mathematics and physics and also a lot of curiosity in order to be able to notice the unusual or unexpected behaviour of the system, in fact study the system, and being able to describe it in a precise and obvious way.
Like in the case of discovery of topological phases of matter, if the researchers did not know topology before studying the system and of course did not study the system very precisely and with curiosity, they could never discover these new phases of matter.