Nowhere dense sets and real-valued functions with closed graphs
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 Gδ subsets of completely regular and normal spaces are characterized. It is also shown that th...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000013 |
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| _version_ | 1832555456652902400 |
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| author | Ivan Baggs |
| author_facet | Ivan Baggs |
| author_sort | Ivan Baggs |
| collection | DOAJ |
| description | 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 Gδ
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. |
| format | Article |
| id | doaj-art-3b984d1c026b4bb0954e0f91bb336e03 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3b984d1c026b4bb0954e0f91bb336e032025-02-03T05:48:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-011211810.1155/S0161171289000013Nowhere dense sets and real-valued functions with closed graphsIvan Baggs0Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Alberta, CanadaClosed 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 Gδ 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.http://dx.doi.org/10.1155/S0161171289000013 |
| spellingShingle | Ivan Baggs Nowhere dense sets and real-valued functions with closed graphs International Journal of Mathematics and Mathematical Sciences |
| title | Nowhere dense sets and real-valued functions with closed graphs |
| title_full | Nowhere dense sets and real-valued functions with closed graphs |
| title_fullStr | Nowhere dense sets and real-valued functions with closed graphs |
| title_full_unstemmed | Nowhere dense sets and real-valued functions with closed graphs |
| title_short | Nowhere dense sets and real-valued functions with closed graphs |
| title_sort | nowhere dense sets and real valued functions with closed graphs |
| url | http://dx.doi.org/10.1155/S0161171289000013 |
| work_keys_str_mv | AT ivanbaggs nowheredensesetsandrealvaluedfunctionswithclosedgraphs |