| Title:
|
Sto let Baireovy věty o kategoriích (Czech) |
| Title:
|
Centenary of Baire’s category theorem (English) |
| Author:
|
Netuka, Ivan |
| Author:
|
Veselý, Jiří |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
232-256 |
| . |
| Category:
|
math |
| . |
| MSC:
|
01Axx |
| MSC:
|
54E52 |
| idZBL:
|
Zbl 1052.54511 |
| . |
| Date available:
|
2010-12-11T18:06:27Z |
| Last updated:
|
2012-08-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141040 |
| . |
| Reference:
|
[Ba1] Baire, R.: Sur les fonctions discontinues qui se rattachent aux fonctions continues.C. R. Acad. Sci. Paris 126 (1898), 1621–1623. |
| Reference:
|
[Ba2] Baire, R.: Sur les fonctions de variables réelles.Ann. Math. Pure Appl. 3 (1899), 1–123. |
| Reference:
|
[Ba3] Baire, R.: Sur la théorie des fonctions discontinues.C. R. Acad. Sci. Paris 129 (1899), 1010–1013. |
| Reference:
|
[Ba4] Baire, R.: Leçons sur les fonctions discontinues.Gauthier-Villars, Paris 1905. |
| Reference:
|
[Ba5] Baire, R.: Projet de calandrier mensuel fixe.Revue Scientifique 59 (1921), 233–240. |
| Reference:
|
[Ba6] Baire, R.: Sur l’origine de la notion de semi-continuité.Bull. Soc. Math. France 55 (1927), 141–142. MR 1504912 |
| Reference:
|
[Ba7] Baire, R.: Oeuvres scientifiques (P. Lelong, ed.).Gauthier-Villars, Paris 1990. |
| Reference:
|
[BaSt] Banach, S., Steinhaus, H.: Sur le principe de la condensation de singularités.Fund. Math. 9 (1927), 50–59. |
| Reference:
|
[Bo] Boas, R. P.: A primer of real functions.Mathematical Association of America, Washington, D. C. 1981. Zbl 0473.26002, MR 0652482 |
| Reference:
|
[Br] Bruckner, A. M.: Differentiation of Real Functions.Amer. Math. Soc., Providence, RI 1994. Zbl 0796.26004, MR 1274044 |
| Reference:
|
[Da] Dauben, J. W.: Georg Cantor. His Mathematics and Philosophy of the Infinite.Princeton University Press, Princeton NJ 1990. Zbl 0858.01028, MR 1082146 |
| Reference:
|
[DeG] De Guzmán, M.: Differentiation of integrals in ${\mathbb {R}}^n$.Lecture Notes in Mathematics 481, Springer, Berlin 1975. MR 0457661 |
| Reference:
|
[Du] Dugac, P.: Sur les fondaments de l’analyse de Cauchy à Baire.Thèse pour obtenir le grade de Docteur ès Science, l’Université Pierre et Marie Curie, Paris 1978. |
| Reference:
|
[Ga] Garg, K. M.: On a residual set of continuous functions.Czech. Math. Journal 95 (1970), 537–543. Zbl 0217.37204, MR 0268334 |
| Reference:
|
[GoPe] Goffman, C., Pedrick, G.: First course in functional analysis.Prentice-Hall, Inc., Englewood Cliffs, N. J. 1965. Zbl 0122.11206, MR 0184064 |
| Reference:
|
[Gr1] Gruber, P. M.: Results of Baire category type in convexity (Goodman, J. E., ed.).In: Discrete geometry and convexity, Ann. New York Acad. Sci., 440, New York Acad. Sci., New York 1985, s. 163–169. MR 0809203 |
| Reference:
|
[Gr2] Gruber, P. M.: Baire categories in convexity.In: Handbook of Convex Geometry, Vol. A, B (Gruber, P. M., Wills, J. M., eds.). North-Holland, Amsterdam 1993, s. 1327–1346. Zbl 0791.52002, MR 1243011 |
| Reference:
|
[Cho] Choquet, G., Marsden, J., Lance, T., Gelbart, S. eds.: Lectures on analysis, vol I.–III.W. A. Benjamin, New York 1969. |
| Reference:
|
[JeKr] Jelínek, J., Král, J.: Note on sequences of integrable functions.Czech. Math. Journal 13 (1963), 114–126. MR 0152619 |
| Reference:
|
[KaSt] Katznelson, Y., Stromberg, K.: Everywhere differentiable, nowhere monotone functions.Amer. Math. Monthly 81 (1974), 349–354. Zbl 0279.26007, MR 0335701 |
| Reference:
|
[KiSz] Kierst, S., Szpilrajn, E.: Sur certaines singularités des fonctions analytiques uniformes.Fund. Math. 14 (1933), 276–294. Zbl 0008.07401 |
| Reference:
|
[KlNe] Klíma, V., Netuka, I.: Smoothness of a typical convex function.Czech. Math. Journal 31 (1981), 569–572. MR 0631603 |
| Reference:
|
[KNV] Král, J., Netuka, I., Veselý, J.: Teorie potenciálu II.SPN, Praha 1972. |
| Reference:
|
[Ku] Kuratowski, K.: Some remarks on the origins of the theory of functions of a real variable and of the descriptive set theory.Rocky Mountain J. Math. 10 (1980), 25–33. Zbl 0437.26002, MR 0573859 |
| Reference:
|
[Le] Lebesgue, H.: Recherches sur la convergence des séries de Fourier.Math. Ann. 61 (1905), 251–280. MR 1511346 |
| Reference:
|
[Ma] Malý, J.: Where the continuous functions without unilateral derivatives are typical.Trans. Amer. Math. Soc. 283 (1984), 169–175. MR 0735414 |
| Reference:
|
[Me1] Medvedev, F. A.: Očerki istorii teorii funkcij dějstvitělnogo peremennogo.Nauka, Moskva 1975. |
| Reference:
|
[Me2] Medvedev, F. A.: Francuzskaja škola teorii funkcij i množestv na ruběže 19.–20. vekov.Nauka, Moskva 1976. MR 0532180 |
| Reference:
|
[NeVe] Netuka, I., Veselý, J.: Harmonic continuation and removable singularities in the axiomatic potential theory.Math. Ann. 234 (1978), 117–123. MR 0481063 |
| Reference:
|
[Or1] Orlicz, W.: Z teorji równania różniczkowego ${y^{\prime }=f(x,y)}$ — Zur Theorie der Differentialgleichung ${y^{\prime }=f(x,y)}$.Bull. Int. Acad. Polon. Sci. Sér. A (1932), 221–228. |
| Reference:
|
[Or2] Orlicz, W.: Metoda kategorii Baire’a w zastosowaniu do pewnych zagadnień analizy matematycznej.Wiadom. Mat., Roczniki PTM, Ser. II (1982), 1–15. MR 0705608 |
| Reference:
|
[Os] Osgood, W.: Non uniform convergence and the integration of series term by term.Amer. J. Math. 19 (1897), 155–190. MR 1505734 |
| Reference:
|
[Ox] Oxtoby, J. C.: Measure and category: a survey of the analogies between topological and measure spaces.Springer, New York 1980. Zbl 0435.28011, MR 0584443 |
| Reference:
|
[Pi] Pier, J.-P. ed.: Development of mathematics 1900–1950.Birkhäuser Verlag, Basel 1994. Zbl 0796.00016, MR 1298630 |
| Reference:
|
[Pr] Preiss, D.: The work of Professor Jarník in real analysis.In: Life and work of Vojtěch Jarník (1897–1970), Novák, B. ed., Prometheus, Praha 1999, s. 55–65. |
| Reference:
|
[PrZa] Preiss, D., Zajíček, L.: On Dini and aproximate Dini derivates of typical continuous functions.KMA Preprint Ser. 1999-13, Charles University, Praha (URL adresa: http://www.karlin.mff.cuni.cz/katedry/kma/kma.html). MR 1825518 |
| Reference:
|
[Re] Renfro, D. L.: Some supertypical nowhere differentiability results for $C[0,1]$.Ph. D. Thesis. N. Carolina State Univ., Raleigh, NC 1993. MR 2690002 |
| Reference:
|
[Ru] Rudin, W.: Analýza v reálném a komplexním oboru.Academia, Praha 1977. MR 0497401 |
| Reference:
|
[Sa1] Saks, S.: On the functions of Besicovitch in the space of continuous functions.Fund. Math. 19 (1932), 211–219. Zbl 0005.39105 |
| Reference:
|
[Sa2] Saks, S.: Remark on the differentiability of the Lebesgue indefinite integral.Fund. Math. 22 (1934), 257–261. Zbl 0009.10602 |
| Reference:
|
[Vo] Volterra, V.: Alcune osservazioni sulle funzioni punteggiate discontinue.Giornali di Math. 19 (1881), 76–86. |
| Reference:
|
[We] Weil, C. E.: On nowhere monotone functions.Proc. Amer. Math. Soc. 56 (1976), 388–389. Zbl 0327.26004, MR 0396870 |
| Reference:
|
[Za1] Zajíček, L.: The differentiability structure of typical functions in $C[0,1]$.Real Anal. Exchange 13 (1987/88), 93, 113–116, 119. |
| Reference:
|
[Za2] Zajíček, L.: Porosity and $\sigma $-porosity.Real Anal. Exchange 13 (1987/88), 314–350. MR 0943561 |
| Reference:
|
[Za3] Zajíček, L.: Porosity, derived numbers and knot points of typical continuous functions.Czech. Math. Journal 39 (1989), 45–52. MR 0983482 |
| Reference:
|
[Za4] Zajíček, L.: Differentiability properties of typical continuous functions.Real Anal. Exchange 25 (1999/00), 149–158. |
| . |
