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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1207.0330 |
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| _version_ | 1866914664674230272 |
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| author | Daher, Mohammad Saadi, Khalil |
| author_facet | Daher, Mohammad Saadi, Khalil |
| contents | In this paper, we show that there are a totally ordered compact K separable (K is Rosenthal compact set), a Hausdorff topology T' on C(K) and two closed subspaces Y1, Y2 of (C(K); Tp) such that (C(K);T') is not universally measurable, (C(K),Tp) = (Y1,Tp) + (Y2,Tp);(Y1,Tp) is isomorphic to (Y2,Tp), (Yj ,Tp) = (Yj,T'), j=1,2; and Bor((C(K)XC(K),T'XT')) is not equal to Bor(C(K)),T'))XC(K)),T')) this is the main result of this work. We start this work to construct totally ordered non metrisable compact sets K(E) from a reference set E which is totally ordered, and from a positive Borel measure on E satisfying some reasonable assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_0330 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Geometric properties of some totally ordered compact sets Daher, Mohammad Saadi, Khalil Functional Analysis 46B50 In this paper, we show that there are a totally ordered compact K separable (K is Rosenthal compact set), a Hausdorff topology T' on C(K) and two closed subspaces Y1, Y2 of (C(K); Tp) such that (C(K);T') is not universally measurable, (C(K),Tp) = (Y1,Tp) + (Y2,Tp);(Y1,Tp) is isomorphic to (Y2,Tp), (Yj ,Tp) = (Yj,T'), j=1,2; and Bor((C(K)XC(K),T'XT')) is not equal to Bor(C(K)),T'))XC(K)),T')) this is the main result of this work. We start this work to construct totally ordered non metrisable compact sets K(E) from a reference set E which is totally ordered, and from a positive Borel measure on E satisfying some reasonable assumptions. |
| title | Geometric properties of some totally ordered compact sets |
| topic | Functional Analysis 46B50 |
| url | https://arxiv.org/abs/1207.0330 |