A characterization of pseudocompactness
It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000264 |
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| _version_ | 1832564133319409664 |
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| author | Prabduh Ram Misra Vinodkumar |
| author_facet | Prabduh Ram Misra Vinodkumar |
| author_sort | Prabduh Ram Misra |
| collection | DOAJ |
| description | It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X. |
| format | Article |
| id | doaj-art-89aa66dd2a134dd0b4675ca9804fe522 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-89aa66dd2a134dd0b4675ca9804fe5222025-02-03T01:11:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014240740910.1155/S0161171281000264A characterization of pseudocompactnessPrabduh Ram Misra0Vinodkumar1I.M.F., U.F.G., Caixa Postal – 597, Goiânia 74000, Go, BrazilI.I.T., New Delhi, IndiaIt is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.http://dx.doi.org/10.1155/S0161171281000264PseudocompactβXz-filterz-ultra function. |
| spellingShingle | Prabduh Ram Misra Vinodkumar A characterization of pseudocompactness International Journal of Mathematics and Mathematical Sciences Pseudocompact βX z-filter z-ultra function. |
| title | A characterization of pseudocompactness |
| title_full | A characterization of pseudocompactness |
| title_fullStr | A characterization of pseudocompactness |
| title_full_unstemmed | A characterization of pseudocompactness |
| title_short | A characterization of pseudocompactness |
| title_sort | characterization of pseudocompactness |
| topic | Pseudocompact βX z-filter z-ultra function. |
| url | http://dx.doi.org/10.1155/S0161171281000264 |
| work_keys_str_mv | AT prabduhrammisra acharacterizationofpseudocompactness AT vinodkumar acharacterizationofpseudocompactness AT prabduhrammisra characterizationofpseudocompactness AT vinodkumar characterizationofpseudocompactness |