### An example of a Darboux function having no fixed points.

Zbigniew Grande
Source: Real Anal. Exchange Volume 28, Number 2 (2002), 375-380.

#### Abstract

In this article we construct an example of a bilaterally quasicontinuous Darboux function $f:[0,1] \to [0,1]$, which has no fixed points.

First Page:
Primary Subjects: 26A05, 26A15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.rae/1184963801
Mathematical Reviews number (MathSciNet): MR2009760
Zentralblatt MATH identifier: 1045.26001

### References

J. B. Brown, Almost continuous Darboux functions and Reed's pointwise convergence criteria, Fund. Math. 86 (1974), 1–17.
Mathematical Reviews (MathSciNet): MR352358
A. M. Bruckner, Differentiation of real functions, Lectures Notes in Math. 659, Springer-Verlag, Berlin 1978.
Mathematical Reviews (MathSciNet): MR507448
Z. Grande, On some special notions of approximate quasi-continuity, Real Anal. Exch. 24 No. 1 (1998–99), 171–184.
Mathematical Reviews (MathSciNet): MR1691744
Project Euclid: euclid.rae/1300906021
S. Kempisty, Sur les fonctions quasicontinues, Fund. Math. 19, (1932), 184–197.
T. Neubrunn, Quasi-continuity, Real Anal. Exch. 14 No. 2 (1988–89), 259–306.
Mathematical Reviews (MathSciNet): MR995972
Zentralblatt MATH: 0679.26003
F. D. Tall, The density topology, Pacific J. Math. 62 (1976),.275–284.
Mathematical Reviews (MathSciNet): MR419709
Project Euclid: euclid.pjm/1102867878