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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| 格式: | Final Year Project |
| 語言: | English |
| 出版: |
Nanyang Technological University
2022
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| 在線閱讀: | https://hdl.handle.net/10356/156902 |
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| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | 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. |
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