## Real Analysis Exchange

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1300108082

Mathematical Reviews number (MathSciNet)
MR3016401

Zentralblatt MATH identifier
1244.54033

#### Citation

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. https://projecteuclid.org/euclid.rae/1300108082

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