On Stone's representation theorem
Given a compact Hausdorff space X, we consider its regular open algebra, i.e. the Boolean algebra of all regular open subsets of X, RO(X). By Stone’s Representation Theorem, every Boolean algebra A is isomorphic to the clopen algebra of S(A), where S(A) denotes the Stone space of A. This thesis p...
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| Format: | Final Year Project (FYP) |
| Language: | English |
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Nanyang Technological University
2022
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| Online Access: | https://hdl.handle.net/10356/156902 |
| _version_ | 1824457146029309952 |
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| author | Loo, Dong Lin |
| author2 | Tang Wee Kee |
| author_facet | Tang Wee Kee Loo, Dong Lin |
| author_sort | Loo, Dong Lin |
| collection | NTU |
| description | Given a compact Hausdorff space X, we consider its regular open algebra, i.e.
the Boolean algebra of all regular open subsets of X, RO(X). By Stone’s
Representation Theorem, every Boolean algebra A is isomorphic to the clopen
algebra of S(A), where S(A) denotes the Stone space of A. This thesis presents
characterisations of the following three items: isomorphism of RO(X), Boolean
embedding of RO(X) and quotient spaces of S(RO(X)). Analogues of the
last two characterisations in the space of continuous real-valued functions on
S(RO(X)) are presented. Some of our results are new and generalize previous
known results. |
| first_indexed | 2025-02-19T04:05:21Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/156902 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T04:05:21Z |
| publishDate | 2022 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1569022023-02-28T23:19:49Z On Stone's representation theorem Loo, Dong Lin Tang Wee Kee School of Physical and Mathematical Sciences WeeKeeTang@ntu.edu.sg Science::Mathematics Given a compact Hausdorff space X, we consider its regular open algebra, i.e. the Boolean algebra of all regular open subsets of X, RO(X). By Stone’s Representation Theorem, every Boolean algebra A is isomorphic to the clopen algebra of S(A), where S(A) denotes the Stone space of A. This thesis presents characterisations of the following three items: isomorphism of RO(X), Boolean embedding of RO(X) and quotient spaces of S(RO(X)). Analogues of the last two characterisations in the space of continuous real-valued functions on S(RO(X)) are presented. Some of our results are new and generalize previous known results. Bachelor of Science in Mathematical Sciences 2022-04-27T06:33:37Z 2022-04-27T06:33:37Z 2022 Final Year Project (FYP) Loo, D. L. (2022). On Stone's representation theorem. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/156902 https://hdl.handle.net/10356/156902 en MATH/21/067 application/pdf Nanyang Technological University |
| spellingShingle | Science::Mathematics Loo, Dong Lin On Stone's representation theorem |
| title | On Stone's representation theorem |
| title_full | On Stone's representation theorem |
| title_fullStr | On Stone's representation theorem |
| title_full_unstemmed | On Stone's representation theorem |
| title_short | On Stone's representation theorem |
| title_sort | on stone s representation theorem |
| topic | Science::Mathematics |
| url | https://hdl.handle.net/10356/156902 |
| work_keys_str_mv | AT loodonglin onstonesrepresentationtheorem |