Real Analysis Exchange

On upper and lower β-continuous multifunctions

Takashi Noiri and Valeriu Popa

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Abstract

In this paper the authors define a multifunction \(F:X \mapsto Y\) to be upper (respectively, lower) \(\beta\)-continuous if \(F^+(V)\) (resp. \(F^-(V))\) is \(\beta\)-open in \(X\) for every open set \(V\) of \(Y\). They obtain some characterizations and several properties concerning upper (resp. lower) \(\beta\)-continuous multifunctions. The relationships between these multifunctions and quasi continuous multifunctions are investigated.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 362-376.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515228

Mathematical Reviews number (MathSciNet)
MR1433621

Zentralblatt MATH identifier
0899.54015

Subjects
Primary: 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]

Keywords
β-open β-continuous quasicontinuous multifunctions

Citation

Popa, Valeriu; Noiri, Takashi. On upper and lower β-continuous multifunctions. Real Anal. Exchange 22 (1996), no. 1, 362--376. https://projecteuclid.org/euclid.rae/1338515228


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