Real Analysis Exchange

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

Joanna Czarnowska

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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

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

First available in Project Euclid: 27 June 2008

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Mathematical Reviews number (MathSciNet)

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

connectedness Darboux property


Czarnowska, Joanna. /mathcal{F}-Connectivity and Strong /mathcal{F}-Connectivity of Multivalued Maps. Real Anal. Exchange 26 (2000), no. 2, 559--580.

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