Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HA230000 Specialized Education 数学通論II スウガクツウロンニ Fundamental Concepts of Mathematics II ISHIHARA KAI イシハラ　カイ Higashi-Hiroshima 2nd-Year,  Second Semester,  3Term (3T) Weds1-2,Fri3-4：SCI E104 Lecture Lecture using blackboard 2.0 J : Japanese 2 : Undergraduate Low-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics Topological spaces, continuous maps, product topology, quotient topology, connectivity, Separation axioms, compactness, bases for topological spaces, metrization Mathematics（Knowledge and Understanding）・Understanding classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.（Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). Studying fundamentals of topological spaces lesson 1. Definition of topological spacelesson 2. Open and closed setslesson 3. Continuous maps lesson 4. Relative topologylesson 5. Product topologyBases for topological spaces amd the Second Axiom of Countability lesson 6. Quotient topologylesson 7. Compactnesslesson 8. Compact spacelesson 9. Midterm examlesson 10. Connectivitylesson 11. Path-connectivitylesson 12. Separation Axiomslesson 13. Hausdorff spacelesson 14. Axiom of countabilitylesson 15. Metrization theoremThe midterm and final exams will be held in the normal class time and place. Textbook: N/A Reference books: M. Umehara and S. Ichiki, Naive set theory and general topology (Shokabo), F. Uchida, Set theory and general topology (Shokabo), S. Morita, Sets and topological spaces (Asakura-shoten),K. Matsuzaka, Introduction to sets and topology (Iwanami-shoten) Blackboard lesson 1.  Review of  the definition and examples of topological spaceslesson 2.  Review of  the definitions of open and closed setslesson 3.  Review of the definitions of continuous mapslesson 4.  Review of the definition of relative topologylesson 5.  Review of the definition of product topologylesson 6.  Review of the definition of quotient topologylesson 7.  Review of the definition of compact spaceslesson 8.  Review of the properties of compact spaceslesson 9.  Review of the midterm exam questions and answerslesson 10.  Review of the definition of connective spaceslesson 11.  Review of the definition of  path-connective spaceslesson 12.  Review of the definition of Separation Axiomslesson 13.  Review of the definition of Hausdorff spacelesson 14.  Review of the definition of Axiom of Countabilitylesson 15.  Review of the metrization theorem Evaluation will be based on exams and class activities. Please fill in the class improvement questionnaire which is carried out on all classes.Instructors will reflect on your feedback and utilize the information for improving their teaching.
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