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Nowhere dense sets and real-valued functions with closed graphs

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  • Ivan Baggs

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.

Suggested Citation

  • Ivan Baggs, 1989. "Nowhere dense sets and real-valued functions with closed graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:748723
    DOI: 10.1155/S0161171289000013
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