Section 1: Introduction page 1
Section 2: Proof of Theorem 2.3 page 2
Section 3: Proof of Theorem 2.2 page 3
Section 4: References

[1] M. J. Greenberg and J. R. Harper, Algebraic topology: a first course, Addison-Wesley, 1981, pp.16-20.
[2] C. R. F. Maunder, Algebraic topology, Van Nostrand Reinhold Company, 1970, p.27.
[3] J. R. Munkres, Topology, Prentice Hall, Incorporated, 2000.
[4] D. Y. Yan, Lecture note of algebraic topology in National Tsing Hua University, 2012.