Real Analysis Exchange

/mathcal{F}-Connectivity and Strong /mathcal{F}-Connectivity of Multivalued Maps

Joanna Czarnowska

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Abstract

In the paper the general connectivity property is given for multivalued maps and the Darboux property, the intermediate value property, functional connectivity property, connectivity property etc. are considered as subcases of this property. This general property is characterized locally, so as corollaries we obtain local characterization of the Darboux property, the intermediate value property etc. for multivalued maps and for real functions those classical results given by Bruckner, Ceder [2] and Garret, Nelms and Kellum [5]. Characterization of the sets of Darboux points, the intermediate value property points etc. for multivalued maps and for real functions are straightforward corollaries from one general theorem (Theorem 11).

Article information

Source
Real Anal. Exchange, Volume 26, Number 2 (2000), 559-580.

Dates
First available in Project Euclid: 27 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1214571350

Mathematical Reviews number (MathSciNet)
MR1844136

Subjects
Primary: 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]

Keywords
connectedness Darboux property

Citation

Czarnowska, Joanna. /mathcal{F}-Connectivity and Strong /mathcal{F}-Connectivity of Multivalued Maps. Real Anal. Exchange 26 (2000), no. 2, 559--580. https://projecteuclid.org/euclid.rae/1214571350


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References

  • A. M. Bruckner, Differentiation of Real Functions,
  • A. M. Bruckner, J. G. Ceder, Darboux continuity, Jber. Deutsch. Math. Verein., 67 (1965), 93–117.
  • J. Ceder, Characterizations of Darboux selections, Rend. Circ. Mat. Palermo, 30 (1981), 461–470.
  • J. Czarnowska, Functional connectedness and Darboux property of multivalued functions, Period. Math. Hung., 26 (1993), No.2, 101–110.
  • B. D. Garrett, D. Nelms, K. R. Kellum, Characterizations of connected real functions, Jber. Deutsch. Math.-Verein., 73 (1971), 131–137.
  • J. M. Jastrzębski, J. M. Jędrzejewski, Functionally connected functions, Zeszyty Naukowe Politechniki Śląskiej, Mat.-Fiz. 48 (1986), 73–79.
  • K. Kuratowski, Topology, Moscov, (1969).
  • J. S. Lipiński, On Darboux points, Bull. Acad. Pol. Sci. Serie Math. Astr. Phys. 26 (11) (1978), 869–873.
  • H. Rosen, Connectivity points and Darboux points of real functions, Fund. Math. 89 (1975), 265–269.