Quantification of topological concepts using ideals
We introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005439 |
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| _version_ | 1832553536667254784 |
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| author | Robert Lowen Bart Windels |
| author_facet | Robert Lowen Bart Windels |
| author_sort | Robert Lowen |
| collection | DOAJ |
| description | We introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces. |
| format | Article |
| id | doaj-art-42082e0dc6174356a2a982f46b7b8c6f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-42082e0dc6174356a2a982f46b7b8c6f2025-02-03T05:53:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126956157910.1155/S0161171201005439Quantification of topological concepts using idealsRobert Lowen0Bart Windels1Department of Mathematics and Computer Science, University of Antwerp-RUCA, Groenenborgerlaan 171, Antwerpen 2020, BelgiumDepartment of Mathematics and Computer Science, University of Antwerp-RUCA, Groenenborgerlaan 171, Antwerpen 2020, BelgiumWe introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces.http://dx.doi.org/10.1155/S0161171201005439 |
| spellingShingle | Robert Lowen Bart Windels Quantification of topological concepts using ideals International Journal of Mathematics and Mathematical Sciences |
| title | Quantification of topological concepts using ideals |
| title_full | Quantification of topological concepts using ideals |
| title_fullStr | Quantification of topological concepts using ideals |
| title_full_unstemmed | Quantification of topological concepts using ideals |
| title_short | Quantification of topological concepts using ideals |
| title_sort | quantification of topological concepts using ideals |
| url | http://dx.doi.org/10.1155/S0161171201005439 |
| work_keys_str_mv | AT robertlowen quantificationoftopologicalconceptsusingideals AT bartwindels quantificationoftopologicalconceptsusingideals |