Porosity, derived numbers and knot points of typical continuous functions

Luděk Zajíček

Czechoslovak Mathematical Journal (1989)

  • Volume: 39, Issue: 1, page 45-52
  • ISSN: 0011-4642

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Zajíček, Luděk. "Porosity, derived numbers and knot points of typical continuous functions." Czechoslovak Mathematical Journal 39.1 (1989): 45-52. <http://eudml.org/doc/13753>.

@article{Zajíček1989,
author = {Zajíček, Luděk},
journal = {Czechoslovak Mathematical Journal},
keywords = {typical continuous functions; knot points; Dini derivates of continuous functions; derived number; porous set},
language = {eng},
number = {1},
pages = {45-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Porosity, derived numbers and knot points of typical continuous functions},
url = {http://eudml.org/doc/13753},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Zajíček, Luděk
TI - Porosity, derived numbers and knot points of typical continuous functions
JO - Czechoslovak Mathematical Journal
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 1
SP - 45
EP - 52
LA - eng
KW - typical continuous functions; knot points; Dini derivates of continuous functions; derived number; porous set
UR - http://eudml.org/doc/13753
ER -

References

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  1. A. M. Bruckner, J. Haussermann, 10.1007/BF01955016, Acta Math. Hungar. 45 (1985), 7-13. (1985) Zbl0592.26010MR0779511DOI10.1007/BF01955016
  2. A. M. Bruckner, B. S. Thomson, Porosity estimates for the Dini derivatives, Real Analysis Exchange 9 (1983-84), 508-538. (1983) Zbl0579.26004MR0766077
  3. K. M. Garg, On a residual set of continuous functions, Czechoslovak Math. J. 20 (95) (1970), 537-543. (1970) Zbl0217.37204MR0268334
  4. J. Haussermann, Porosity characterizations of intersection sets with the typical continuous function, Real Analysis Exchange 9 (1983-84), 386-389. (1983) MR0766065
  5. P. D. Humke, M. Laczkovich, 10.1090/S0002-9939-1985-0784172-7, Proc. Amer. Math. Soc. 94, (1985), 244-248. (1985) Zbl0564.26002MR0784172DOI10.1090/S0002-9939-1985-0784172-7
  6. P. D. Humke, T. Vessey, Another note on σ -porous sets, Real Analysis Exchange 8 (1982-83), 261 - 271. (1982) Zbl0543.28001MR0694514
  7. V. Jarník, Über die Differenzierbarkeit stetiger Funktionen, Fund. Math. 21 (1933), 48-58. (1933) Zbl0007.40102
  8. V. Jarník, Sur les nombres dérivés approximatifs, Fund. Math. 22 (1934), 4-16. (1934) Zbl0008.14903
  9. B. S. Thomson, Some theorems for extreme derivates, J. London Math. Soc. (2), 27 (1983), 43-50. (1983) Zbl0523.26004MR0686501
  10. B. S. Thomson, Real Functions, Lect. Notes in Math. 1170, Springer-Verlag 1985. (1985) Zbl0581.26001MR0818744
  11. L. Zajíček, Sets of σ -porosity and sets of σ -porosity, (q), Časopis Pěst. Mat. 101 (1976), 350-359. (1976) Zbl0341.30026MR0457731
  12. L. Zajíček, On Dini derivatives of continuous and monotone functions, Real Analysis Exchange 7 (1981-82), 233-238. (1981) Zbl0462.26003MR0657321

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