Naïve Set Theory & its applications

Venue: University of Kashmir, Hazratbal, Srinagar 190006
Dates:      13th April to 2nd May, 2015


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Amin Sofi

S. M. Srivastava

Mailing Address University of Kashmir, Srinagar, 190006 Indian Statistical Institute, Kolkata


Speakers and Syllabus 

  Programme Schedule

 Day Date  Lecture-I
Mon 13.04.2015 BVR MAS SMS

Tue 14.04.2015 BVR MAS BVR MAS
Wed 15.04.2015 BVR MGN MAS BVR
Thu 16.04.2015 MGN MAS MGN MAS
Fri 17.04.2015 MGN MAS MGN MAS
Sat 18.04.2015 BVR MAS MGN BVR
Mon 20.04.2015 BVR MGN MAS BVR
Tue 21.04.2015 MGN HS MGN BVR
Wed 22.04.2015 HS SMS MGN HS
Thu 23.04.2015 SG RB SG RB
Fri 24.04.2015 RB SG RB SG
Sat 25.04.2015 SMS HS SMS HS
Mon 27.04.2015 HS SMS HS SMS
Tue 28.04.2015 SG HS SG HS
Wed 29.04.2015 RB SG RB SG
Thu 30.04.2015 SMS RB SMS RB
Fri 01.05.2015 RB SMS SG RB
Sat 02.05.2015 SG SMS Distribution of certificates & valedictory


  • RB- Rana Barua
  • SG-Sreela Ganopadhyay
  • MGN-M.G.Nadkarni (Measure Theory)
  • BVR-B.V.Rao(Measure Theory)
  • HS-H.Sarbadhikari (Set Theory)
  • MAS-M.A.Sofi (Metric Topology)
  • SMS-S.M.Srivastava (Set Theory)

3. Resource Persons:

  1. Rana Baura, ISI Kolkatab.
  2. Sreela Ganopadhyay, ISI Kolkatad.
  3. M.G.Nadkarni (Measure Theory), CBS, Mumbaif.
  4. B.V.Rao(Measure Theory), CMI, Chennai
  5. Sarbadhikari (Set Theory), ISI Kolkataf
  6. M.A.Sofi (Metric Topology), Kashmir University, Srinagar
  7. S.M.Srivastava (Set Theory), ISI Kolkata


  • S.M.Srivastava: An overview of how Cantor discovered set theory.
  • H.Sarbadhikari: Finite and infinite sets, countable and uncountable sets and standard results on them, definition of |X| = |Y| and |X| ≤ |Y|, X, Y sets and standard results on them, naïve definition of cardinal numbers and cardinal arithmetic. Applications.
  • S. Ganopadhyay: Well ordered sets, proofs and definitions by transfinite induction, comparability of well ordered sets, naïve definition of ordinal numbers, trichotomy theorem of well ordered sets, well ordering sets of ordinal numbers, limit and successor ordinal numbers, countable ordinals, the first uncountable ordinal 1 , alephs, continuum hypothesis and generalized continuum hypothesis. Applications.
  • M.A.Sofi: Metric spaces and their topology, complete and separable metric spaces, continuous and uniformly continuous functions, Pasting lemma, compact metric spaces, compactness in R , continuous maps on compact metric spaces, extension of (a) continuous functions from subsets of metric/normal spaces (b) homeomorphisms from compact subsets of R.
  • Rana Barua: partially ordered sets, axiom of choice, well ordering principle and Zorn’s lemma, equivalence of three axioms, Applications.
  • M.G.Nadkarni: Poincare recurrence theorem, Banach-Tarski paradox, Glimm-Effros dichotomy.
  • B.V.Rao: Measurable spaces and measures, Lebesgue measure, Vitali partition, example of a non- measurable sets, Polish spaces, Baire category theorem and applications, standard Borel spaces.
  • S.M.Srivastava: Cantor-Bendixon derivatives, characterization of countable closed sub-sets, Cantor theorem on sets of uniqueness (an application in Fourier series), Polish groups.


Actual Participants 


S.No Name Gender Institution State Degree/ Position
1 Ratan Kumar Giri M NIT, Rourkela Odisha Ph.D
2 Anand Pratap Singh M ISM,Dhanbad Jharkhand Ph.D
3 Bulusu Naga Vekatesh Satish M ICAS, Kakinada Karnataka Asst.Prof.
4 Firdous Ahmed Shah M Kashmir Univ, S. Campus J&K Asst.Prof.
5 Ravi Kumar M C. Univ of Hyderabad Telengana Ph.D
6 T. Kalimani M Govt.Arts College, Thiruvalluvar T.N. Ph.D
7 Dilip Kumat Pradhan M Rourkela Univ. Odisha Ph.D
8 S. Arunagirinathan M Govt.Arts College, Thiruvalluvar T.N. Ph.D
9 Mohd Saleem Lone M CUK, Srinagar J&K M.Phil
10 Shameek Paul M CBS, Mumbai Maharashtra Ph.D
11 Pratush Kumar M ISM,Dhanbad Jharkhand Ph.D
12 Sushil Sangli M Shiv Nadir Univ.,Noida U.P. M.Sc
13 Mushtaq Ahmed Bhat M Kashmir Univ, Srinagar J&K Ph.D
14 Mujeeb Ahmed Kawoosa M A.S. College, Srinagar J&K Asst. Prof.
15 Khalid Nazir M Kashmir Univ, S. Campus J&K Ph.D
16  Nisar Ahmed Lone M Govt. Degree Col, Pulwama J&K Asst. Prof.
17 Bisma Zahoor M F Kashmir Univ, Srinagar J&K M.Phil
18 Sumaira Shafi F Kashmir Univ, S. Campus J&K M.Phil
19 Shaista Bashir F Kashmir Univ, S. Campus J&K M.Phil
20 Asma Rafiq Sofi F Kashmir Univ, S. Campus J&K M.Phil
21 Fida Hussain M Kashmir Univ, S. Campus J&K M.Phil
22 Manzoor Ahmed Zargar M Kashmir Univ, S. Campus J&K M.Phil
23 Sameer Ahmed Gupkari M A.S.College, Srinagar J&K Asst. Prof.


 How to reach

Depending upon the modes of travel from other parts of the country to Srinagar, one has the following

1. By Air: From the airport to the university campus situated in Hazratbal, one can hire a cab/radio taxi which would charge something like Rs.700-800/. There are several university campuses in Srinagar & the taxi driver shall have to be told to take him/her to the Kashmir University campus at Hazratbal-(Dargah, as it is popularly known locally).
2. Those coming by train/air upto Jammu & plannig to travel to Srinagar by road (Taxi/bus/private car) usually end up at the TRC (Tourism Reception Centre) in Srinagar from where one can take an autorickshaw to the Kashmir university campus as explained above. Since the charges as quoted by the driver can in general be negotiated, the normal charges should not exceed Rs.250/.