위상수학I 강의록 페이지입니다.

made by 김명일(2001년),고영우,문종면,남기훈 (2005년2학기)

추가및 수정 김선화,이주현 (2009년1학기)

1. Basic concepts
   
   
   1. Metric space [ps] [pdf] [TeX]
   2. Topological space, basis and subbasis [ps] [pdf] [TeX]
   3. Interior and Closure [ps] [pdf] [TeX]
   4. Properties of Continuous Functions [ps] [pdf] [TeX]
   5. Subspace and Product space [ps] [pdf] [TeX]
   6. Homeomorphism and Embedding
      Homeomorphism [pdf] [tex]
      Embedding[ps] [pdf]
   7. Cantor set and Space filling curve [tex] [pdf]    [Cantor set Flash movie]
   
   
2. Basic topological properties
   
   1. Separation axioms [pdf] [tex]
   2. Compactness[pdf] [tex]
   3. Tychonoff theorem [pdf] [tex]
   4. Connectedness [pdf] [TeX]
   5. Axioms of countability [pdf] [TeX]
   
   
3. Metric space
   
   1. Compact metric space[pdf] [TeX]
   2. Complete metric space[pdf] [TeX]
   3. Completion of a metric space[pdf] [TeX]
   
   
4. Normal space
   
   1. Normal space[pdf] [tex]
   2. Urysohn lemma[pdf] [tex]
   3. Uryshon metrization theorem
      Hilbert cube & Hilbert space[pdf] [tex]
      Urysohn embedding & metrization theorem[pdf] [tex]
   4. Tietze extension theorem[pdf] [tex]
   5. AR and ANR[pdf] [tex]
   
   
5. Further topics
   
   1. Paracompactness[pdf] [tex]
   2. Local compactness [pdf] [tex]
   3. Quotient space[pdf] [tex]
   4. Baire space
      Baire space and category[pdf] [tex]
      Existance of nowhere differentiable functions[pdf] [tex]