Nowhere dense sets and real-valued functions with closed graphs

Ivan Baggs

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-8

Abstract:

Closed and nowhere dense subsets which coincide with the points of discontinuity of real-valued functions with a closed graph on spaces which are not necessarily perfectly normal are investigated. Certain G δ subsets of completely regular and normal spaces are characterized. It is also shown that there exists a countable connected Urysohn space X with the property that no closed and nowhere dense subset of X coincides with the points of discontinuity of a real-valued function on X with a closed graph.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:748723

DOI: 10.1155/S0161171289000013

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