| Title:
|
Porosity, derived numbers and knot points of typical continuous functions (English) |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1989 |
| Pages:
|
45-52 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A24 |
| idZBL:
|
Zbl 0672.26002 |
| idMR:
|
MR983482 |
| DOI:
|
10.21136/CMJ.1989.102277 |
| . |
| Date available:
|
2008-06-09T15:25:05Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102277 |
| . |
| Reference:
|
[1] A. M. Bruckner, J. Haussermann: Strong porosity features of typical continuous functions.Acta Math. Hungar. 45 (1985), 7-13. Zbl 0592.26010, MR 0779511, 10.1007/BF01955016 |
| Reference:
|
[2] A. M. Bruckner, B. S. Thomson: Porosity estimates for the Dini derivatives.Real Analysis Exchange 9 (1983-84), 508-538. MR 0766077, 10.2307/44153566 |
| Reference:
|
[3] K. M. Garg: On a residual set of continuous functions.Czechoslovak Math. J. 20 (95) (1970), 537-543. Zbl 0217.37204, MR 0268334 |
| Reference:
|
[4] J. Haussermann: Porosity characterizations of intersection sets with the typical continuous function.Real Analysis Exchange 9 (1983-84), 386-389. MR 0766065, 10.2307/44153551 |
| Reference:
|
[5] P. D. Humke, M. Laczkovich: Typical continuous functions are virtually nonmonotone.Proc. Amer. Math. Soc. 94, (1985), 244-248. Zbl 0564.26002, MR 0784172, 10.1090/S0002-9939-1985-0784172-7 |
| Reference:
|
[6] P. D. Humke, T. Vessey: Another note on $\sigma$-porous sets.Real Analysis Exchange 8 (1982-83), 261 - 271. MR 0694514, 10.2307/44151592 |
| Reference:
|
[7] V. Jarník: Über die Differenzierbarkeit stetiger Funktionen.Fund. Math. 21 (1933), 48-58. 10.4064/fm-21-1-48-58 |
| Reference:
|
[8] V. Jarník: Sur les nombres dérivés approximatifs.Fund. Math. 22 (1934), 4-16. 10.4064/fm-22-1-4-16 |
| Reference:
|
[9] B. S. Thomson: Some theorems for extreme derivates.J. London Math. Soc. (2), 27 (1983), 43-50. Zbl 0523.26004, MR 0686501 |
| Reference:
|
[10] B. S. Thomson: Real Functions.Lect. Notes in Math. 1170, Springer-Verlag 1985. Zbl 0581.26001, MR 0818744 |
| Reference:
|
[11] L. Zajíček: Sets of $\sigma$-porosity and sets of $\sigma$-porosity.(q), Časopis Pěst. Mat. 101 (1976), 350-359. MR 0457731 |
| Reference:
|
[12] L. Zajíček: On Dini derivatives of continuous and monotone functions.Real Analysis Exchange 7 (1981-82), 233-238. MR 0657321, 10.2307/44153409 |
| . |
