The Linear Space of Hausdorff Continuous Interval Functions
In this paper we discuss the algebraic structure of the space H(X) of finite Hausdorff continuous interval functions defined on an arbitrary topological space X. In particular, we show that H(X) is a linear space over R containing C(X), the space of continuous real functions on X, as a linear subsp...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2013-12-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/207 |
| _version_ | 1797726030596669440 |
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| author | Jan Harm van der Walt |
| author_facet | Jan Harm van der Walt |
| author_sort | Jan Harm van der Walt |
| collection | DOAJ |
| description | In this paper we discuss the algebraic structure of the space H(X) of finite Hausdorff continuous interval functions defined on an arbitrary topological space X. In particular, we show that H(X) is a linear space over R containing C(X), the space of continuous real functions on X, as a linear subspace. In addition, we prove that the order on H(X) is compatible with the linear structure introduced here so that H(X) is an Archimedean vector lattice. |
| first_indexed | 2024-03-12T10:39:56Z |
| format | Article |
| id | doaj.art-a1e2d0597c2b47348e97187894abf3fc |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T10:39:56Z |
| publishDate | 2013-12-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-a1e2d0597c2b47348e97187894abf3fc2023-09-02T08:16:04ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182013-12-012210.11145/j.biomath.2013.11.261140The Linear Space of Hausdorff Continuous Interval FunctionsJan Harm van der Walt0Department of Mathematics and Applied Mathematics, University of PretoriaIn this paper we discuss the algebraic structure of the space H(X) of finite Hausdorff continuous interval functions defined on an arbitrary topological space X. In particular, we show that H(X) is a linear space over R containing C(X), the space of continuous real functions on X, as a linear subspace. In addition, we prove that the order on H(X) is compatible with the linear structure introduced here so that H(X) is an Archimedean vector lattice.http://www.biomathforum.org/biomath/index.php/biomath/article/view/207Interval functionsvector spacevector lattice |
| spellingShingle | Jan Harm van der Walt The Linear Space of Hausdorff Continuous Interval Functions Biomath Interval functions vector space vector lattice |
| title | The Linear Space of Hausdorff Continuous Interval Functions |
| title_full | The Linear Space of Hausdorff Continuous Interval Functions |
| title_fullStr | The Linear Space of Hausdorff Continuous Interval Functions |
| title_full_unstemmed | The Linear Space of Hausdorff Continuous Interval Functions |
| title_short | The Linear Space of Hausdorff Continuous Interval Functions |
| title_sort | linear space of hausdorff continuous interval functions |
| topic | Interval functions vector space vector lattice |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/207 |
| work_keys_str_mv | AT janharmvanderwalt thelinearspaceofhausdorffcontinuousintervalfunctions AT janharmvanderwalt linearspaceofhausdorffcontinuousintervalfunctions |