Real Analysis Exchange

Classification of Points of Lower Semi-continuity of a Multifunction in Topological Spaces

Hiranmay Dasgupta and Saibal Ranjan Ghosh

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In this paper we introduce the notion of $y$-lower semi-continuity and point out a distinction between a point of lower semi-continuity in global sense and a point of lower semi-continuity in local sense in general topological spaces after classifying points of $y$-lower semi-continuity (resp. lower semi-continuity) and also study their interrelationships. In particular, we find a necessary and sufficient condition for a bijective open multifunction on a $T_{2}$ space to be lower semi-continuous. Finally, a sufficient condition for an open bijective multifunction on the real line to have at most countable points of lower semi-discontinuity is formulated.

Article information

Real Anal. Exchange, Volume 36, Number 1 (2010), 29-44.

First available in Project Euclid: 14 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54C05: Continuous maps 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
Secondary: 54A99: None of the above, but in this section

lower semi-continuity lower semi-discontinuity \textity-l.s.c. \textity-l.s.d. $s_y$-point $w_y$-point honest point \textits-point \textitw-point \textitc-point


Ghosh, Saibal Ranjan; Dasgupta, Hiranmay. Classification of Points of Lower Semi-continuity of a Multifunction in Topological Spaces. Real Anal. Exchange 36 (2010), no. 1, 29--44.

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