Naïve Set Theory & its applications

  Programme Schedule

• 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.

 How to reach

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

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/.