On Pervin's example concerning the connected-open topology
Irudayanathan and Naimpally [1] introduced a topology for function spaces (called the connected-open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin [2] gave an example showing that the proviso cannot be weakened...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000333 |
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| _version_ | 1832556071513751552 |
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| author | T. B. M. McMaster |
| author_facet | T. B. M. McMaster |
| author_sort | T. B. M. McMaster |
| collection | DOAJ |
| description | Irudayanathan and Naimpally [1] introduced a topology for function spaces (called the connected-open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin [2] gave an example showing that the proviso cannot be weakened to normality. The purpose of this note is to point out a lacuna in his demonstration, and to re-establish the validity of the example. |
| format | Article |
| id | doaj-art-70c51aee43074990b7e75064421b3959 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-70c51aee43074990b7e75064421b39592025-02-03T05:46:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113222322610.1155/S0161171290000333On Pervin's example concerning the connected-open topologyT. B. M. McMaster0Pure Mathematics Department, Queen's University, Belfast BT7 1NN, IrelandIrudayanathan and Naimpally [1] introduced a topology for function spaces (called the connected-open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin [2] gave an example showing that the proviso cannot be weakened to normality. The purpose of this note is to point out a lacuna in his demonstration, and to re-establish the validity of the example.http://dx.doi.org/10.1155/S0161171290000333function spaceconnected-open topologycomplete normality. |
| spellingShingle | T. B. M. McMaster On Pervin's example concerning the connected-open topology International Journal of Mathematics and Mathematical Sciences function space connected-open topology complete normality. |
| title | On Pervin's example concerning the connected-open topology |
| title_full | On Pervin's example concerning the connected-open topology |
| title_fullStr | On Pervin's example concerning the connected-open topology |
| title_full_unstemmed | On Pervin's example concerning the connected-open topology |
| title_short | On Pervin's example concerning the connected-open topology |
| title_sort | on pervin s example concerning the connected open topology |
| topic | function space connected-open topology complete normality. |
| url | http://dx.doi.org/10.1155/S0161171290000333 |
| work_keys_str_mv | AT tbmmcmaster onpervinsexampleconcerningtheconnectedopentopology |