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...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/156902 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| id |
sg-ntu-dr.10356-156902 |
|---|---|
| record_format |
dspace |
| spelling |
sg-ntu-dr.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 |
| institution |
Nanyang Technological University |
| building |
NTU Library |
| continent |
Asia |
| country |
Singapore Singapore |
| content_provider |
NTU Library |
| collection |
DR-NTU |
| language |
English |
| topic |
Science::Mathematics |
| spellingShingle |
Science::Mathematics Loo, Dong Lin On Stone's representation theorem |
| 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. |
| author2 |
Tang Wee Kee |
| author_facet |
Tang Wee Kee Loo, Dong Lin |
| format |
Final Year Project |
| author |
Loo, Dong Lin |
| author_sort |
Loo, Dong Lin |
| title |
On Stone's representation theorem |
| title_short |
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_sort |
on stone's representation theorem |
| publisher |
Nanyang Technological University |
| publishDate |
2022 |
| url |
https://hdl.handle.net/10356/156902 |
| _version_ |
1759858420073103360 |