BITS-PILANI,HYDERABAD CAMPUSINSTRUCTION DIVISION

FIRST SEMESTER 2013-2014Course Handout (Part II)

Date: 01/08/2013In addition to part-I (General Handout for all courses appended to the timetable) this portiongives further specific details regarding the course.

Course No. : MATH C331/MATH F311Course Title : INTRODUCTION TO TOPOLOGYInstructor-in-charge : M.S. Radhakrishnan

1. Course Description: Metric Spaces; Topological Spaces – subspaces; Continuity andhomeomorphism; Quotient spaces and Product spaces; separation axioms; Urysohn’s lemmaand Tietze extension theorem; Connectedness; Compactness; Tychonoff’s Theorem; LocallyCompact Spaces; Homotopy and the fundamental group.

2. Scope and Objective of the Course: To introduce the students to concepts of logicalthinking in abstract terms using formal and axiomatic methods and to lay the foundations forfurther studies in abstract mathematics.

“ Don't just read it; fight it! Ask your own questions, look for your ownexamples, discover your own proofs. Is the hypothesis necessary? Is theconverse true? What happens in the classical special case? What about thedegenerate cases? Where does the proof use the hypothesis? ”

3. Text Book: Munkres, J.R.: Topology, PHI (Second Edition), 20004. Reference Books:

1. Albert Wilansky, Topology for Analysis, Xerox2. John L. Kelley, General topology., van Nostrand. Reprinted (1976) by Springer

Verlag3. L. A. Steen and J. A. Seebach, Counterexamples in topology, Springer, 1978.4. C. Wayne Patty, Foundations of Topology, Second Edition, Jones & Bartlett,

2009

5. Course Plan:Lec.No.

Topics to be Covered Ref. To text book:Sec.

1-2 Sets and Functions 1-103-4 Topological Spaces; Examples 125 Basis and subbasis 136 Subspaces & Subspace Topology 167 Finite Products 158-9 Closed sets and limit points 17

10-11 Continuous functions; homeomorphisms 1812-13 Arbitrary products 1914-16 Metric topology 20-2117-18 Quotient topology 2219-21 Connectedness & its Importance 23-25

P.T.O.

22-24 Varieties of Compactness 26-2825-26 Locally Compact spaces 2927-29 Countability axioms 3030-32 Separation axioms 3133-34 Normal spaces; Urysohn’s lemma 32-3335 Urysohn Metrization Theorem 3436-38 Tychonoff’s Theorem; Completely Regular Spaces 3739-40 Homotopy of Paths 5141-42 The Fundamental Group 52

6. Evaluation Scheme:ECNo.

Evaluation Component Duration Weightage Date, Time Nature ofComponent

1. Test I 60 min 24% 27/9, 5.00 -- 6.00PM

CB

2. Test II 60 min 24% 12/11, 5.00 --6.00 PM

OB

3. Quizzes-announced/unannounced

12% Dates may beannounced in theclass

CB

4. ComprehensiveExamination

3 hrs 40% 03/12 ,2.00 –5.00 PM

CB

7. Make-up Policy: Make-up will be given only for very genuine cases and prior permissionhas to be obtained from I/C.

8. Chamber consultation hours: To be announced in the class.

9. Notices: The notices concerning this course will be displayed on the LTC Notice Boardonly.

Instructor-in-chargeMATH C331