Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMA1010 | Modern Aspects in Topology and Measure Theory |
| Teaching Staff in Charge |
Assoc.Prof. ANISIU Valeriu, Ph.D., anisiu math.ubbcluj.ro |
| Aims |
|
The course containes more advanced topics in topology and measure theory not included in
the standard course in real analysis |
| Content |
|
Filters and nets.
Separation axioms (T3,T4). Product spaces, Tychonov@s theorem. Compactifications. Metrizability of topological spaces. The Weierstrass-Stone theorem. Classification of some topological spaces using Venn diagrams. Convergences for sequences of measurable functions; classical theorems L^p spaces. Fourier series, Dirichlet and Fejer kernels, pointwise convergence. Real measures, Radon-Nikodym@s theorem. Derivation for measures, singular measures, applications. Measure and integration in product spaces, Fubini@s theorem Topological groups, Haar measures Hausdorff measures, fractals. |
| References |
|
1. V. Anisiu: Topologie şi teoria măsurii. Universitatea $Babeş-Bolyai$ Cluj-Napoca, 1995
2. G.B. Folland: Real Analysis. Modern Techniques and their applications. Wiley, 1999 3. H.L. Royden : Real Analysis, 3rd ed, MacMillan, New York, 1988 4. C. George: Exercises in integration. Springer, 1984 5. L.A. Steen, J.A. Seeback: Counterexamples in Topology. Springer, 1978 6. J. Munkres: Topology, 2nd ed. Prentice Hall, 2000 7. C. Swartz: Measure, integration and function spaces. Word Scientific, 1994 8. P. Kree: Integration et theorie de la mesure. Une approche geometrique. Ellipses, Paris, 1997 9. W. Rudin: Real and Complex Analysis. McGraw-Hill, 1986 |
| Assessment |
|
Midterm test and Final Exam.
|
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |